I'll try to answer your question, sorry if it doesn't satisfy you.

Ottoman relations with Ming China were almost entirely commercial. The Ottoman nobility especially liked Chinese blue and white porcelain and so it was widely sought after for status symbol. One particular Küçük Beşir for example was recorded owning 1397 porcelain bowls and plates of Chinese origin. This wide demands also made Ottoman artisans to produce ceramic imitations of Chinese porcelain, sometimes with their own unique style. Iznik and Kütahya stood out as major ceramic producers, and the finest of their goods were considered a good substitute for Chinese porcelain.

But that, as far as i know is as far as relations go. However, Ottoman (and one Persian) authors who have or never visited China made literature describing Ming China for one reason or another, and that, i think, still counts as interactions. I will briefly describes three literature made that describes China in one way or another

Khitayname

In 1516, Ali Ekber Khitayi, a merchant from Transoxiana, composed a travel account on China. For a travel book, this was ordinary enough as it follows the usual pattern of the 'exotic' far east like many other travellers to China. It is the earliest and most comprehensive account on China written for the Ottoman court discovered so far. Khitayi opens his book with a description of the topography of the Arabian Peninsula, Anatolia, Iran, and Transoxiana. He argues that these places are the hub of the world because they are inhabited by Muslims. Afterwards Khitayi covers Chinese geography, describes three major caravan routes leading to China from the Ottoman lands, and discusses the Chinese government, administration, military, society and customs in detail. At the end of the book, Khitayi states that he completed his account in May 1516 in Istanbul, which suggests that Khitayi prepared it for Selim I. However, the dedication in the introduction addresses the Ottoman sultans in general and particularly Süleyman the Magnificient. This inconsistency suggests that Khitayi actually prepared the work for Selim I, but after Selim died unexpectedly in 1520, he changed the dedication and decided to present the work to Süleyman I. This book was made to introduce China to the Ottoman court and portrays China as a worthy model for a universal empire. He uses China as an example by which the Ottoman sultans, could magnify their imperial power, bring order to imperial possessions and assure the Ottoman sultan the universality of his empire with a mirror image he articulated through China.

In Khitayi's words, China is an empire where cultural diversity and religious coexistence through imperial patronage are eminent, territorial expansion happens through just wars, and wealth and justice are diffused evenly throughout the empire. In his descriptions of the wealth of China, Khitayi emphasizes its abundant resources ranging from rice, wheat, wood, and ceramics to luxury goods such as gold, silver, and silk. He maintains that the residents of the towns and cities build tall warehouses to store these resources. Khitayi also claims that the wealth of the country is not concentrated in one region, but rather is diffused equally to all parts of the country. He asserts that what has made China rich and prosperous for such a long time is its disciplined army and the just rule of the Chinese emperors. Chinese rulers, he argues, did not initiate a war unless it was justified and unless it was certain that their armies would win. On law and customs, Khitayi asserts that the wealth and prosperity of China was brought in part for Chinese respect for old customs and imperial law. He frequently reminds the reader that thanks to the strict observance of imperial orders and old customs and traditions, China was a prosperous and rich country. When he refers to the organization and administration of towns, cities, military service, and daily life, he maintains that both in daily life in the towns and villages and in the army, everybody knew their duties and responsibilities. If they did not follow the law, they will be punished in the worst possible way. He maintains that in China members of families did not show forgiveness to each other when one of them committed a crime. A son would even denounce his father if his father acted against the law. Khitayi concludes that this should be the way in Islamic custom as well. Khitayi also praises the Chinese army for its unbeatable tactics and weapons. He highlights Chinese soldiers’ docility and discipline, their respect for their commanders, and their strict observance of the hierarchy of rank. Last but not least, he portrays China as a diverse multi-religion country where people of all religions, especially Muslims were tolerated. Khitayi devotes a large section to the different religions practiced in China during the Ming dynasty, especially in the early sixteenth century, and underlines that Muslims of China had prestige and status in Chinese society. He maintains that the Chinese emperor, Kin Tay (The Zhengde Emperor) had been very friendly with the Muslims and had Muslim warlords under his service. He also recounts that the eunuchs of the Chinese palace are all Muslims who can practice their faith without any limitations and relates a "popular story" that the son of Kin Tay Khan converted to Islam after seeing Muhammad in his dream and finding the shahada inscribed on his wall in green letters.

Kitab-i Tevarih-i Padishahan-i Vilayet-i Hindu ve Hitay

In the 1580s, a provincial treasurer during Murad III's reign named Seyfi Çelebi compiled a work depicting the history, geography, economic life, customs, and rulers of China, India, Transoxiana, and Iran. The work contains nine chapters, the first of which is about China. Just like Khitayi before him, he mainly emphasizes justice, Muslims, wealth and prosperity in China. He reports that there are many Muslims in China and that one of the previous emperors (possibly referring to the Zhengde Emperor) converted to Islam after seeing a vision of Muhammad in a dream. The author asserts that many Muslims had lived in China for a long time and that there are around three hundred mosques in one of the provinces. Then he describes the Chinese palace, which, he maintains, consists of the residence of the Chinese emperor, as well as valleys and waterways. He claims that the Chinese emperor travels on these waterways by ship and organizes hunting parties at the gardens of his palace. He also claims that the Chinese palace is so large that the emperor needs seven thousand eunuchs to serve him. He finalizes his chapter on China with a description of its abundant riches. He claims that there are so many gold and silver mines in China, but only fifty of them are working, whereas the others are closed. Had all of them been working, there would be no demand for gold and silver any more, and nobody would care about them. Compared to Khitayi's detailed account, Seyfi's account is much shorter. This is because his book is mainly to teach the Ottoman sultan the history of Central Asia and the genealogies of Muslim rulers of India, Transoxiana, and Iran. (1/2)

(2/2)

Cihannüma

Katip Çelebi's magnum opus in 1648 also contained description of China, though it's rather complicated because he struggled with sources. Within a century of the consolidation of the Ming Dynasty, China had turned inward. A period of exploration and discovery initiated by the Yongle Emperor during his reign was rolled back, and the access of merchants and representatives from distant countries was increasingly limited to carefully managed border entrepots. Because of that, he heavily relies on European and Muslim sources from the previous centuries. Because of that, he repeated the error of China-Cathay that European authors made at the time. Even though Khitayi's Khitayname had been correctly describes China as one country, he was unimpressed with his book because of his preference on European and older Islamic text. He wrote:

The Persian Qanunname, which I think was written by a merchant and presented to Sultan Selim II, records that China and Cathay form a single country with a total of 12 divisions. But as drawn on the globe and as recorded in the geography books, China and Cathay are independent sultanates and separate countries, each having defined borders. Therefore I have paid no heed to the words of that ignorant person, which is mostly idle talk, nor to the stories connected with the clime of Cathay that are recorded there, nor to the statement that the clime of China is without divisions

Nevertheless, despite his openly-stated bias, it is clear that Katip Çelebi could not completely dismiss the Khitayname, because European sources didn't contain detailed information on China and that he deemed a Muslim work to be trustworthy and so he combined information from the Khitayname with an older Timurid book called the Ruzname, which is also about China. As a result of this frankenstein-monster attempt, he presents a confused and overlapping portrayal of the different regions of China along with the peoples of the steppelands and deserts that surrounded it. The characteristics of his sources led him to divide his discussion of the region into two separate chapters. The first of dealt with the region that he believed to be "China" (Çîn), and a second, lengthier chapter dealt with what he called "the clime of Khitây" (which in European works is "Cathay", a word that likely has roots in the earlier Khitan peoples). However it becomes increasingly clear that Katip Çelebi was, at least part of the time, describing elements of the Ming Dynasty from two separate perspectives, while erroneously presenting these perspectives as a description of two separate kingdoms

His description on China is rather short and confused, For example here's how he attempted to describe the capital of China:

All authors are in agreement that this city borders on the north with Tatar and Cathay. It is said to be the throne of both the emperor of China and the khan of Cathay. Its circumference is 100 Italian miles. It has several hundred stone bridges, constructed high enough that large ships with sails spread can pass underneath them. There is a large lake in the interior of the city, seven miles in circumference, with two islands, on each of which a great palace has been built for the emperor. It was related from Mârkûs (Marco Polo) that 30,000 soldiers are permanently stationed there to guard the city. But these descriptions do not accord with common sense. And some say that after Marcos this city was destroyed and no longer remains in this state

Here we can see that his belief based on European sources is challenged. If China and Cathay are two separate countries, how come they have the same capital? But Katip Çelebi noted that his European sources are in conflict and dismissed Marco Polo's accounts as "do not accord with common sense". The irony is that in siding with the viewpoints expressed in the European sources, he ignored clues in his Muslim sources who had correctly understood that much of China and Cathay were one and the same. He also describes how the Chinese made porcelain and the high value of it, noting that the finest of the pieces were acquired by the Chinese Emperor and forbidden to be exported. He concluded by noting the special qualities of porcelain, such as its supposed ability to purify liquids, its imperviousness to aging, its resistance to scratching by any substance save diamonds, its health value in "increasing the intellect" when drinking wine from it, and its extraordinary artistic properties, notably that painting and designs on it could sometimes be viewed only when held up to the light.

Now things started to pick up when dealing with Cathay. His narrative is basically a mix of references to the Chinese Ming Dynasty and older references to the steppeland beyond China's borders. For example when describing how the Cathayan military worked:

Their rule in fighting is that when they are one stage away from the enemy, they line up their carts around them and in one hour, dig a trench in front of them. Their combat is very severe. They draw the line [of carts] in front of the soldiers who stand ready with gun in hand. First they fire their cannon, then they fire ... the guns. They only suffer defeat when they are making camp or breaking camp. If the enemy attacks then, and they are unable to draw their carts in front of them or to their side, he will achieve victory. In fact, a brave commander of the Kalmyks named Esen Tayşi with 60,000 troops attacked the Khıtây Khaqân Chîn-Khûâr in 854/1450, broke them by this means and took him prisoner. Ever since this battle, the Khaqân has not gone to war in person but sends the army wherever necessary

Which clearly refers to the T'umu Crisis where an Oirat army decimated Ming Chinese army under the young Zhengtong Emperor. Despite his critical shortcomings, he managed to somewhat describe 15th century Ming under another name. He describes the opening of the Forbidden City in Beijing, and the process of entering the country and registering with the Chinese authorities. He also discussed the well-organized post-stages necessary to travel to the imperial capital, including its rapid communication networks, along with the names of the major cities encountered along the way and their prominent architectural sites and characteristics. Additionally, he also describes the Ming court and its ceremonial practices as witnessed by the Timurid emissaries. He portrays Cathay as a prosperous, well-administered empire but not a good country to open relations with. He relates an incident where a horse that was brought by the emissaries as a gift for the Yongle Emperor (which he refers to as Daymeng, a corruption of Chinese term for sub-prefect) ended up throwing him off and injuring him, which nearly got the Timurid emissaries imprisoned and executed. Luckily, their Muslim translators and guests at the Ming court were able to intercede on their behalf, and after explaining that the horse was given because it had once belonged to Temür himself, the emissaries were able to receive gifts and depart. He describes the people and ruler of Cathay as Buddhists, but they maintained good relationship with its Muslim subject per the usual narrative. In his words:

They call Muhammad—peace be upon him—shîn-chîn, meaning "best of the people". They have an affection for Islam and Muslims. The call to prayer is made five times a day in their lands. The Muslims wear turbans and perform the congregational prayer. One day the commanders assembled and said: “Thousands of Muslim households are mixed with ours. Let us eradicate them. They do not give wealth such that they would be considered beneficial.” The Khaqan said: “Our forefathers never acted in this way, so how can we? We judge them according to their manifest behavior. At present, there is no manifest denier among them, and what have we to do with their hidden thoughts?

He concludes that the Khitayans are broad-minded in matters of religion and know nothing of fanaticism whatever their religious belief may be, as their effort in this world is to abide by the law. He then goes on to note the existence of Jewish, Christian and Muslim places of worship in the realm. He also describes a grand canal, the customs of Cathayan people which pretty much the customs of Turko-Mongol nomadic peoples of Central Asia, and the Kalmyks, who either fought against or submitted to the ruler of Cathay depending on circumstances. The old Mongol capital of Karakorum was also mentioned as being under the rule of Cathay as well.

Sources/Further Reading

Relocating the Center of the Universe: China and the Ottoman Imperial Project in the Sixteenth Century by Pınar Emiralioğlu

Living the Good Life: Consumption in the Qing and Ottoman Empires of the Eighteenth Century by Suraiya Faroqhi

Other Places: Ottomans Traveling, Seeing, Writing, Drawing The World by John J. Curry et al