The amount of Khazars who converted to Judaism make up a small amount of todays Jewish DNA pool
Again most European Jews are an admixture of EE converts to the faith and Greco-Roman jews and some Mid East Jews.
The " Jews are actually Khazars" theory is just one of the shameful episodes of the Muslim World in last century
You don't understand Turkic history and culture. The ethnicity follows that of the father. What matters is the progenitor father. Turks conquered form east to west, the army would generally take locals as wives and then their children again would either take regional locals or take wives from the lands they further pushed into. So if i have a half English son, that son then marries an Indian, has a son, then that son marries a Korean but has a son, as far as Turk culture is concerned he is a Turk. The genetic markers will have diluted, but in Turk culture the father is ethnicity.
It had to be this way for Turks because the Turks were like Vikings on steroids. While the Vikings descended down from norway, denmark and swept into europe. The Turks descended down from siberia and swept across, china, india, persia, across the entire euroasian land mass, conquered the roman capital, even went to the border of morocco.