Without a "when" to pin down a time period, there are going to be multiple answers to this question! I will assume the post-Tanzimat era for my answer.

In the mid-to-late 19th centruy, some Ottoman bureaucrats who administered the empire, sought to promote a form of Ottoman identity ("Ottomanism") that could be shared by all, irrespective of ethnic or religious affiliation. Leaving aside the sincerity or effectiveness of this project, we can at the very least see that they left an "Ottoman presence" in the far-flung provinces of the Empire.

As a first example, one of the most famous of these figures was Mithat Paşa, a reformist appointed to serve as a vilayet administrator of Baghdad, Tuna (Danube Province) and Nish (part of present-day Serbia). Mithat Paşa was a believer in showing the benefits of the Ottoman state in provincial centres and as such he established Ottoman schooling systems wherever he went and embarked on infrastructure projects to improve the local economy, most notably in Baghdad.

Right into the 20th century, you can find Ottoman students educated first in provincial centres, travelling to Istanbul to complete their education at the state's primary institutions of education. And with a little effort in the Ottoman archives, you also find records of educated officials appointed to postings in regions far from their homes. One case that I am familiar with, for example, has a Christian from today's Turkish-Iraqi border region, working as a government clerk in Kosovo.

One of my favourite signals of how the Ottomans attempted to demonstrate the state's reach throughout the Empire was in the construction of clocktowers. Even today you can see these Ottoman-era clocktowers in prominent squares of cities like Izmir, Aleppo (I believe it has survived), Jaffa (ie Tel Aviv), Plovdiv and so on. Interestingly, the construction of several of these was assisted by funds collected by local groups seeking to honour their city. The railroad building projects of the same period also sought to bring the provinces of the Empire "closer", particularly the Hejaz railway.

Another example of an attempt to bring the Ottoman state to the locals was in the provincial press, an endeavor that began in the 1860s. The government set up printing presses in many provincial capitals and would publish multilingual newspapers for the local populace. Ottoman Turkish was always one of the languages, but depending on the region, they would also be published in others: Bulgarian, Serbian, Arabic, Armenian, Armeno-Turkish and so on. The journal Selanik in today's Thessaloniki was printed in four languages: Ottoman Turkish, Greek, Ladino and Bulgarian.

Additionally, because of the Ottoman millet system, Istanbul was the religious centre of all the major faiths in the Empire; besides the mufti and chief rabbi, you also had the heads of the Orthodox, Armenian, Syriac and various Catholic churches all based in the capital. These in turn would have their subordinates (ie archbishops) spread around the Empire, ensuring that there was continued communication with the provinces and the capital, where the the important decisions concerning civil laws affecting your daily life would be made.

As a final point since most of the above comes across as broadly positive, during the Hamidian era the heavily Armenian regions experienced the Ottoman state presence in the form of state-sponsored massacres (the Armenian Genocide again show the reach of the Empire far into the eastern provinces). The Ottoman military was often part of life on the periphery, whether due to wars with neighbours or putting down rebellions, like it did in Yemen in the early twentieth century. Remember that Sultan Albdulhamid was ultimately overthrown by the Balkan units of the Ottoman military marching on the capital in 1908.

There's a lot more to explore beyond the above: the parliamentary elections in the second constitutional era; the judicial system; taxation; conscription; and so on.