Iskender kebap was invented in Prusa (don't know how you call this city) in 1867 by Iskender efendi who was a butcher. So definitely turkish. About doner in general i don't know. The fact is that once i have heard a turkish historian who said (and i completely agree) that ancient turks were nomads and didn't really had a cuisine. The ancient greeks had a cuisine but a poor one. Both ended up having the rich Eastern Roman empire cuisine.

So the same base, just regional differences. That's why i always eat in turkish restaurants when i am abroad. If i come to Turkyie i'll go north to the black sea. My grandmother's family was from there. Never have been there though...