Are you serious right now? Read the quote, it sounds like mongols had a problem with Islam for a long time, someone doesn't just say what the leader of the mongols did out of the blue randomly one day. Also, read this
https://en.m.wikipedia.org/wiki/Byzantine–Mongol_alliance
And yes TURKIC people are probably a mix of middle eastern and mongol but middle East would have had arab input from hundreds of years of complete control and conquest, turks and turcs are not the same thing.
History tells us that invading armies leave genetic input, how much depends on the people, whether they can flee to the suburbs or how tolerant they can be. The romans left genetic input everywhere, arabs left genetic input into all of North Africa and even spain/portugal, there is absolutely NO WAY they didn't leave anything in Middle East, NONE, you cannot be this deluded. We are talking about a time with small populations meaning it was a lot easier to change the dna of a "nation" early on
As for balkans, the slavs left genetic input all the way down to Greece, Bulgaria etc and they weren't even a big empire or massive army. What makes you think the osmans left nothing behind in South Europe with much bigger armies and far more wars, whether you don't think they didn't have Arab father lines like I think you cannot deny genetic input from so many years of conquest, so many men dying, so many people fleeing etc.
For me, most J1, T1a and a few sub clades of e1a/e1b was added to byzantine area from osman conquest, until you can tell me which haplogroups they spread but so far all you have done is deny all input even into middle East from arabs which is complete delusion. And yes I believe south europe would look more "white" today if there was no osman conquest, just not as blonde or ginger like North Europe. There are too many middle eastern looking people in South europe for me to believe the osmans were mongols, they were 100% middle eastern with some Arab father ancestors. Even though mongols had wars in anatolia just look at Turkey today, most of them look like middle eastern people, none look like mongols because mongols time there was short lived whereas osman wasn't
https://en.m.wikipedia.org/wiki/Mongol_invasions_of_Anatolia
Anyway, can you give me some numbers for Yemen, Saudi Arabia, Oman, Iraq and other Arab league nations. I would be interested to see what their haplogroups are