I do wonder, if it is possible that the Turkish people of Modern Day Turkey could have ended up somewhere else besides the Anatolia? Where else could they have ended up?
The first scenario I can think of of WHY their would not be a Turkey or Turkish Empire based in the Anatolia would be their defeat by a resurgent Byzantine Empire. In one short story of the "Sideways in Crime" anthology there was such a scenario. Byzantines got gunpowder early and defeated the Turks and eventually their new empire streched from the Balkans to Baghdad, yet their was still a Turkish Empire in the story. So where else could they have settled? I would suppose the next best hospitable area would be lower Mesopotamia and the Levent. Maybe in Egypt?
The question is where else would the Turks have settled, as in OTL the best choice in reach would be the Anatolia because it is quite fertile compared to the rest of the Middle-East. Whats the next best choice?