The ancient populations included Lydians, Phrygians, Carians, Lycians, Cappadocians, Cilicians, Armenians, and Galatians (Celtic immigrants in the 3rd century B.C.). In the Middle Ages they were mostly Christian and Greek-speaking.
The current population is also partly descended from Muslims who fled from outlying parts of the Ottoman Empire (Ukraine, Hungary, Serbia, Rumania, etc.) as they came under Christian rule, and from Christian boys who were taken from their families in the "blood tribute" in Ottoman times, or from people enslaved by Turkish pirates.
On the other side, there are many Europeans who have remote ancestry from the Middle East, where agriculture was first developed--it's thought that agriculture was brought into Europe by immigrants from the Middle East.
I’m interested in all that, but more in the genetic make-up rather than the language and religion they speak today.
I would like to see it investigated by genetic tests whether the population really does come mostly from people who were there before the Turkish takeover (and before the Roman and Greek conquests as well). I think the change from urban/agricultural to pastoral might’ve led to a big change in the composition of the population, particularly in central Anatolia. The more populated coastal regions I can see remaining relatively unchanged.
Before the Turks, I figure not much changed from the people who were there from prehistoric times, and that the successive invasions just introduced a thin layer of new blood.
However, the Byzantines did a lot of resettlement of captured people, e.g., Slavs from Europe, and of Christians displaced from places conquered by the Muslims, but whether that was enough to make much of a dent in the genetic profile, I don’t know.