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Jews (whether ashkenazi, sephardic, mizrahi or ethiopian) are different from whites, being ashkenazi (Agatha's mom) the closest to europeans with around 50% of their ancestry traced back to europe.
https://i.ibb.co/vP9WwjS/are-jews-white-european-infographic.jpg
As for the khazar theory, there's no substantive evidence of a Khazar origin among Ashkenazi Jews.
https://en.m.wikipedia.org/wiki/Khazar_hypothesis_of_Ashkenazi_ancestry