No Turks in the region at that point in history. Turks are related to Mongols.
Most Turks are decended from the original people of Turkey - a bit like Hungary where it is very hard to find any central asian genetic contribution in the modern Hungarian population. Genes != culture.
Are you saying that modern Turks in Turkey are just Greeks that converted to Islam?
Well not Greeks (in the main), but Anatolians I guess. Certainly not Central Asian.
Although culturally Turks prefer the middle asia hun and monolian origin narrative, they are genetically mostly descendants of the anatolians who happened to live and breed there already for many millenia. Those people didn't suddenly disappear. This contrast between culture and genetics is confusing to many turks (me included)
That's what I think happened to other countries in the region as well. I'm from Iraq and speak Arabic but I don't think my ancestors are from the "Arabian peninsula", we just adopted the language. It also explains why "dialects" of Arabic can be so different.
The study found that ancient Egyptians were ... also closely related to Neolithic populations from the Anatolian Peninsula and Europe.
Maybe Cretan/Hittite could be, but Greek/Turkish, I doubt.
I think the story is that the Ptolemaic Pharaohs were the descentants of Alexander the Great's generals. They created a Hellenistic (=Greek) kingdom in Egypt and the ruling elite most probably was of Greek origin.
Ptolemaic dynasty came over 1000 years later than the mummies analyzed. 300 - 30 BC... Even then, Turkey was mostly Persia or Greece... Turks didn't exist yet.