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To my knowledge Turkic languages originated among Mongoloid people in Xinjiang and mongolia. Then moved westward but the Khazar Khaganate existed BEFORE the Mongols took over north central asia and left their genetics their and BEFORE Mongols expanded their turkic languages west ward.
These lands today are filled with slavs and irano afghans (in case of the east caucasus)
Chasaren.jpg
Mongol empire lasted 1206 till 1368 but was basically done with by 1259 and greatly reduced with low power by 1294.
https://en.wikipedia.org/wiki/Khazars
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