What is called Turkey today didn't exist during the lifetime of St George. Geographically it is still called Asia Minor, and it has seen a lot of states and empires on her ground during the millennia.
Invaded by Turkisk tribes about 1000 A.D., a first Turkish state was founded by Osman I. (1258 - 1326). Therefore the Turkish Empire which spread from Asia Minor to Northafrica, the Balkans, Arabian Peninsula and Persia was called Osmanic. In 1923 modern Turkey was founded in Asia Minor, giving up all non Turkish countries, but including a small part of Europe just across the Bosporus (Rumeli = Roman house, but it means Greek).
Certainly St George wasn't a Turc.

Wilfried