Not according to the times of Israel:
‘Bottleneck’ dates back 600 to 800 years, genome analysis shows; researcher says among population ‘everyone is a 30th cousin’
https://www.timesofisrael.com/ashkenazi-jews-descend-from-350-people-study-finds/
Personally, though, this makes much more sense:
Ashkenazic Jews’ mysterious origins unravelled by scientists thanks to ancient DNA https://theconversation.com/ashkenazic-jews-mysterious-origins-unravelled-by-scientists-thanks-to-ancient-dna-97962
So, to answer your question, could be... Gok-Turks may have been related to Huns.
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