The Jewish proper diaspora began with the Babylonian exile in the 6th century BCE.
After the overthrow of the Kingdom of Judah in 5856 BCE by Babylon and the deportation of a considerable portions of its in habitants to Mesopotamia (which is now Iraq, Turkey, Syria).
The Western Diaspora Greek from the beginning of Hellenistic period took place in Egypt, which is very far from current Turkey.
Under the Roman Empire the diaspora was in Jerusalem.
So the correct answer is Babylonian
