I've released an article in which I identify and discuss various longstanding mysteries of Jewish genomics, in the light of recent published and unpublished research.
The topics include: 1) possible origins of several controversial uniparental lineages found in modern Ashkenazic populations (ydna: Q2a-Y2200, R1a-Y2619, R1a-Z2123, R1b-ZZ12, G2a-Z6552; mtdna: K1a1b1a), 2) 14th Century Erfurt data vis a vis the Khazar Hypothesis, 3) genetic footprint of the Judeo-Greco-Roman-Byzantine mixing event, 4) First Temple ancestries of the Jews of Africa, Yemen, and India, 5) the Sephardic-Ashkenazi phenomenon, 6) whereabouts of Occitanian Jews, and 7) historicity of Biblical genealogies.
The article may be downloaded here: https://www.academia.edu/84138593 (a free account is necessary to download articles from this site, which includes many papers relevant to Jewish genomics).
I hope some or all of the topics may be of interest to you.