Genetic markers cannot determine Jewish descent: https://www.ncbi.nlm.nih.gov/pmc/articles/PMC4301023/
"Although it makes sense that horizontal, intercommunity matings were, as a rule, less frequent than intra-community matings that maintained the vertical branching pattern, there is considerable historical evidence for inter-community mating, at the individual levels (Rabbis invited to serve in far communities, travelers, and emissaries sent to collect money in foreign communities, etc.), as well as at the level of whole communities: Historian Shlomo Sand (The Invention of the Jewish People, Transl. by Yael Lotan. London; New York: Verso.2009) and many others brings evidence of extensive community-wide proselytizing events, from North-Africa all the way to Southern Russia.
The apparent achievement of the children of the priest Aaron in maintaining their distinct status over a very long time and across very diverse socio-geographic distances is even more remarkable, when juxtaposed with that of the remaining children of the tribe of Levi, the Levites.
No haplotype frequently common to Levites was found. But among the Ashkenazi Levites a cluster of haplotypes with a very high degree of relatedness was found. The R-M17 Y-chromosome haplogroup, is rare in Israelite Jewish populations (<5%), and generally rare or absent in populations of the Near East. It is, however, prevalent in Belarusians (50%) and the Slavic-speaking Sorbs (66%). Apparently only Ashkenazi Levites, and not the rest of their fellow Jews, have received a significant male contribution of Slavic origin. Data suggest that the R-M17 chromosomes were transmitted horizontally to Ashkenazi Levites (or the other way round) relatively late, somewhere between the fourth and eleventh century.
However, is it sensible to draw similar conclusions with respect to the Ashkenazi ethnic-group from, say, the clusters of haplotypes of the Ashkenazi Levite? Behar and associates point out that the Levite cluster of R-M17 haplotype is very common in non-Jewish populations of north-east Europe. Thus, isn't it reasonable to assume that the origin of these haplotypes among Levites (and other non-Levite Jews) is in horizontal transmission, namely that male progeny of some non-Jewish Europeans who intermarried with a Jewess (inadvertently) acquired the status of Levites?"
Jewish Genetic Diseases: http://www.jewishgeneticdiseases.org/jewish-genetic-diseases/