Over half of the Jews in Europe have Southern Italian ancestry
(web.archive.org)https://web.archive.org/web/20210126122411/https://geneticliteracyproject.org/2013/10/08/ashkenazi-jewish-women-descended-mostly-from-italian-converts-new-study-asserts/Modern European Jews are from Southern Italy, with Levantine Jews taking on southern Medditerannean wives for over millennia.
Observable through common paternal haplotypes where less than 25% of Y-DNA can be found amongst Arabs from Palestine, Lebanon and Syria. But where 40% or more of m-tDNA suggests Ashkenazi women having ancient Near and Middle Eastern roots.
Therefor over 60% of the genes are of "European" origin; Southern Italy.
Suggesting Jews from the Levant travelled with women and many had Italian brides, as much of the European Jew DNA would suggest through genetic testing.
Genealogical records also suggest a long tradition of Judaism being practised in Southern Italy, with some stages in history being as high as 10% outside of European diaspora where it would have been much, much higher.
Especially after the expulsion in Spain as they almost all fled to the safety of Jew-Italy.