Is there a time in history when the Greeks and Turks fought together in the same team?

To add to Andrei Stoica’s answer—

(Vote #1: User. This is a supplementary answer)

—Byzantines often used Turkish mercenaries, as Andrei pointed out, especially when they went nuts and fought civil wars in the 14th century that only the Ottomans could benefit from. And after the civil wars washed up, and Byzantines were a vassal state of the Ottomans, Byzantines fought as vassals of the Ottomans. But that wasn’t even an alliance, let along an “on the same team”, that was just work for hire.

Like Andrei said: no, never.

(Please read Andrei Stoica’s answer btw. Vote #1: User.)