Simple answer
Direct control - of a small portion of the northern part of the peninsula, from 109 BCE until approximately 311. Indirect control - always.
Detailed answer
Direct control The Chinese have controlled the Korean peninsula from around Pyongyang north. They have invaded the peninsula, and they have conquered a few of the kingdoms there, but they haven't ever controlled a major portion of the peninsula.
Under Emperor Wu, the Chinese decided to bring the frontier regions under direct control. In 109-108 BCE, the Chosun people were conquered and four commanderies, or military barracks/cities were set up. Of the four, only two survived (the other two simply fell into disuse and were merged with the other two) and they were located around present day Pyongyang and along the Yalu river.
The intention of the Chinese in sending armies to conquer Paekche and Koguryo was to bring the entire Korean Peninsula under T'ang imperial control... But Silla was unwilling to accept such an outcome. Accordingly, almost from the moment of Koguryo's collapse Silla launched a fresh campaign, this time in an effort to win control over the former Koguryo domain. Lee p69
In 660, during the Three Kingdoms period (Silla, Paekche, Goguryeo), the Silla kingdom allied with the Tang from China and conquered Paekche. In 668, the Silla and Tang defeated the Goguryeo. Almost immediately, the Silla turned on the Tang and forced them out of the southern portion of Goguryeo (read: the peninsula) and by 676, the Unified Silla kingdom ruled all of the Korean peninsula south of Pyongyang, and the new Parhae (read: the remaining Goguryeo) controlled the rest.
The Goguryeo people were an offshoot of the Puyeo people, and they both lived in present day Manchuria. The Goguryeo were originally located in the Hunhe River basin (present day Shenyang China) from 75 BCE until 207 CE. They were raiders who attacked their neighbors until the Liaodong commandery retaliated and they were forced into the Yalu river valley, setting up near present day Manpo, North Korea (but still on the Chinese side of the river). In the third century, China fell into three rival dynasties and Goguryeo had diplomatic relations with the southern dynasties of Wei. The northern dynasty retaliated by destroying the Goguryeo capital. The Goguryeo disappeared for a time but came back around 300-330, during King Micheon. At this point, Chinese power in Manchuria was falling and the Goguryeo stepped in to fill that void.
According to legend, the Paekche kingdom was founded in 18 BCE. In reality, no one is really sure when they were founded, but it is known to be later than that. The earliest verifiable information from Paekche comes from around 346-375. Legend says it was founded by two brothers who were given land by the lord of the region. One of the brothers became king and his descendants ruled until they were defeated by the Silla/Tang in 660. The much more likely scenario is that Paekche was founded by... Puyeo migrants from... Manchuria! It's important to note that the Paekche didn't really come onto the scene until after the Chinese empire had collapsed in the late 3rd/early 4th centuries.
So what does it mean to be "Korean" or "Chinese"? The Goguryeo people (from whom the Goryeo people took their name, from which "Korea" is derived) were based in Manchuria. The Paekche people were founded by Manchurians. The Silla were allegedly born from eggs, but realistically probably have the same roots as the other kingdoms, i.e. NOT "Korean". At the same time, the commanderies in "Korean" territory were there for such a long time that the cultures and people definitely mixed. Which brings us to...
Indirect control
Tang's interests in Korea were largely strategic, and as it became obvious that Silla posed no threat to its security, relations warmed. China found instead that its policy of using trade and cultural exchanges and offering legitimacy and prestige to the Silla monarchy was effective in keeping Silla safely in the tributary system. Seth p64
The people of the Korean peninsula were barbarians and the Chinese state in 108 BCE was a modern one. The people of the peninsula adopted Chinese culture, politics, traditions, etc. Once the commanderies were set up, local leaders were selected/appointed and the empire was left to run itself by the many kings the emperor named. These kings/kingdoms paid tribute to the Chinese and the kings went to the commanderies to pay the tribute and to receive their clothing and seals from the emperor. After this system fell apart around 300, the Korean Three Kingdoms emerged. During this time, the Sui tried to defeat the Goguryeo and failed (2,800 Sui survived out of a force of 305,000). The Sui dynasty collapsed and the Tang emerged. The Tang then helped out Silla unify the peninsula before being forced out. But it was the cultural influence that they exerted that left a mark. Government policies created by the Tang were adopted by the unified Silla. Former Goguryeo people were welcomed into the Tang government. Trade between the kingdoms was strong.
Also, although the Unified Silla was independent (after expelling the Tang from Korea, the Tang abandoned all plans for Korea), they still paid tribute to China. In fact, tribute was given well beyond Unified Silla, and in many ways. When the Joseon dynasty was founded
Yi Korea used the term sadae ("serving the great") to describe its foreign policy toward Ming China, and every effort was made to maintain a friendly relationship. The pro-Ming policy espoused by Chosun's founder, Yi Song-gye, in the course of his struggle with the old Koryo aristocracy, was necessary as well to confer legitimacy on the authority of the new regime and its ruler... The Yi government dispatched three regular embassies to Ming each year... The purpose of these missions chiefly was political, but they served also as the medium for cultural borrowing and economic exchange. Lee p 189
Lee goes on further to explain how the Ming snubbed Yi for around 200 years by claiming he was the son of an anti-Ming troublemaker.
Lady Ki... had in the previous year given birth to the likely crown prince and was now being crowned formally as an imperial consort to the Yuan emeror. This turn of events could hardly have been imagined two decades earlier, when she was sent as a captive prize of submission to the Mongol rulers. Indeed she and hundreds of other "tribute women" sent to Mongol-controlled China had embodied the Mongol's comprehensive control over the kingdom of Koryeo, a period in Korean history normally viewed with utter shame. *Hwang p51-52
Woman were also sent as tribute. Empress Gi (1315-1370)of the Yuan dynasty was born a Korean and was sent as tribute . (Bonus picture - here is the sign from her tomb explaining her situation.)
This also shows the messiness of saying "did X control Y". China was under the direct control of the Mongols, and Korea was sending tribute to the Chinese, who were now Mongols. At the same time, the Mongol emperor had a son with his Korean wife, thus making the Chinese and the Mongols subjects of a Korean ruler. It's all very messy.
There are other examples of the indirect control exerted by China over Korea all the way until the present. The highlights would be their involvement in the Imjin War against Japan in Korea, their treaty with Japan to inform them of any action they were planning to take in Korea (their failure to do so lead to the first Sino-Japanese War in 1895), the fact that they continued to get involved in Korean politics, for example during the Tonghak rebellion in 1894 and the subsequent war it fought with Japan over the issue. During the Japanese colonial era, the Chinese gave the Korean exile government a home in Shanghai. In 1949 and 1950, Kim Il-sung had to get Mao's approval and support to fight the Korean War.
Korea has accepted and acceded to Chinese control, be it direct or indirect, for virtually all of it's recorded history.
TLDR - I put that at the top, go back and start there.
Sources
Referenced but not cited, Korean History in Maps edited by Michael D. Shin
