I'm absolutely not trying to make you feel foolish or anything, but I need to ask for some clarification. Your phrase "the whole Byzantine Empire" has me a bit confused. Are you aware that the Eastern Roman Empire fell piece by piece over a period of centuries and, in 1453, consisted of little more than the city of Constantinople and some islands in the Aegean?

I'm guessing you are asking what happened to Roman/Greek population of Anatolia after Byzantine Empire fell.

They were mostly assimilated and converted. Most of this assimilation and conversion were not forced but "coerced". Initially when Turks entered Anatolia, they were small in number and did not had the capacity to completely replace Byzantine landholders, so in exchange for conversion, they largely allowed them to keep their lands. There was also Jizya, a tax taken from non-muslims. As long as they paid jizya, they were largely free to keep their religion. There was not a fixed amount, and Padishahs tended to change the amount depending on their view towards religious minorities. For the most part, conversions and such were higher in urban cities, as most merchants did not wish to be in a disadvantage against Turkish or Jewish merchants also trading in the Empire. This Turkification was much weaker in Greece both due to local landholders being richer and more resistant, and also due to Turks controlling Greece for a much shorter duration than Anatolia. These local landholders would later help instigate the Greek War of Independence, but also create problems for the new Greek state that formed after.

By late Ottoman period, most of Anatolia were Turkified, and roughly a couple million Greeks were left, largely located in Aegean, Marmara and Pontic coasts. Nearly entirety of these Greeks were send to Greece in the population exchange immediately after Greco-Turkish War. Currently, around 5 thousand Greeks live in Istanbul, mostly in the Islands offshore.