For example, and not surprisingly, most of Tunisia's collective DNA comes from north Africa and only 4% from Arabia.
Lebanon is much more of a mix, with less than half from Arabia and 14% from Jews:
Ashkanazic Jews themselves are mostly Jewish, not surprisingly, with some admixture from Eastern Europe and Arab countries.
Not surprisingly, Jewish blood is also seen in Spanish communities in the New World.
I have no idea if Sephardic Jews are in any of these samples or at what date in history they judge genes to come from the "Jewish diaspora."
National Geographic offers to do a DNA test on anyone to determine their origins, with the results being added to the database (if you choose.)