Very fascinating topic as I technically am from this gene pool
From all the studies and history, this is what I think:
It’s clearly a mix dna of European and Middle Eastern
The male side - the research shows very Middle Eastern
The Female side they can tell from the mitochondria. During the early Roman republic you have many thousands of wornen coverts to Judaism . Many of the female origins are Italian !!!
Now in USA : you have 60 percent intermarriage , so this topic becomes very mute!!
I think I am accurate and I hope this topic stays stable
It's an interesting topic,
but mixing politics and DNA is...nothing good ever comes from this, because people tend to address it as some sort of "blood purity test" instead of a tool in historic research.
From what I've studied:
1. Diaspora communities were usually, (Jerba aside), established around core 4-5 families,
of Jewish male refugees and local converted women. Each community can be traced to 4-5 female progenitors. Imagine Israeli slaves, gladiators winning their freedom and establishing networks of communication to build community centers.
2. When DNA test write 'European', in many cases they put Ashkenazi communities under that category without distinction, because that's where Ashkenazi communities are most concentrated physically, not as an indication of their origin. So goes with categories as "Middle Eastern", inside that category are Mizrahi Jews who are concentrated physically there, but that is usually not specified.
3. The local population saw a significant flow of early European DNA prior to the Israelite era, the Hebrews, or Canaanites as they're usually identified and lumped together, were always a mixture, the whole Levant region. Actually for a modern Levantine to have specifically one side, east or west, means late arrival of the community.
4. DNA is not static, certain genes express more strongly in certain climatic environment,
food etc. Even skin pigmentation can change in matters of a single generation. Less evident now, but also attested in Gmarah, is that in pre-exile time, pronunciation of the language, certain throaty letters, is as well function of environment.
5. DNA databases are using categories based on location rather than nations, or ethnicity.
It is a good tool for historic research of a movement of a community, not its origin.
As well most of their categories are based on modern population in a location,
real ancient DNA is relatively scarce for any significant database.
I.e. they go to Saudi Arabia, sift out the most strongly expressed sequences,
and decide these are 'the Arabs'. These categories are based on modern gene pool.
And if the Arabs of old had a different DNA, it would be tossed out as foreign - Nebuhadnezzar did a groat job erasing entire nations moving them places.
6. In order to make a Hebrew database, we have to open the graves of our ancestors, G-d forbid, and we won't do that ever. The only cases this is done is to transfer remains to Israel, not for research. Nobody will let anyone touch the Cave of the Patriarchs and Matriarchs or the mount of Olives.
7. All that said, the main conclusion is that such categories in the modern study help indicate relationships between modern communities based on their current location, and movement rather than origin - and the most extensive researches I've seen show clear clusters between both Ashkenazi and Mizrahi communities with Lebanese Christians and Druze, and the Arab population in the cluster of today's Saudi Arabia, Syrian Muslims and Bedouins.
You would do better researching from which community did Your core family came,
and I don't mean going millenias back, only as far back as emancipation, 17th-18 century Haskalah, and study those communities closer, because at that time most of them they still had family trees and other communal historic accounts (genizah), and were typically clustered in somewhat similarity to the communities in Babylon, i.e. for lack of better term - Judean aristocracy and royalty, like once used to Reish Galutah. Probably as much a half of those communities trace their core back to the family of Rashi and his grandsons. Around this axis one can get a more detailed information and personally accurate about the history of the family.
There were, and still are many Rabbinic courts that keep the names of the communities based on their specific location in the diaspora, these are also the families who still keep family trees, and have much information and records about their community. As well I'd suggest looking into the Hebrew library, I don't remember the name of the books now, but there were several such extended researches and documented in several writings. As well as the archive of Beit Hatfutzot ('house of diasporas') in Israel.
On an ending note - if anyone wants to know his tribal affiliation along these lines,
one can rely on a commonly accepted distinction that was made in Hebrew literature on this subject, of course not as a rule personally, but along the historic lines of the communities - the northern diaspora are the tribe of Binyamin, the southern diaspora are the tribe of Yehudah.