Khazar Strain
The Y-DNA Haplogroup R1a that's been showing up in Ashkenazic Jews at a rate of 8-10% {and Q1b ~ 5%} has been claimed as a Khazar heritage from the First Millennium when a Turkic-speaking confederation ruled the Crimea and much of the Ukraine and then converted to Judaism before disappearing. This R1a is most likely of East-Iranian origination. As stated, the Khazars were a confederation of many peoples including Celts, Goths, Alans, Magyars etc. The ruling tribe spoke a Turkic language, but just as the Seljuks brought a language to Anatolia, like the Hittites thousands of years before them, they did not bring all that much genetic material. Would the Khazars be that different? And given that the Khazar nation originated in the Caucuses they were probably already infused with many of these same Haplogroups which having migrated south, such as the Hurrians, provided many of the ancestors to the original Israelites. For instance, the Székely Peoples of Hungary who may have descended {in part} from the breakaway Khazar tribes, the Kabars, show a relationship of over 21 % to Y-DNA Haplogroup J which is often identified with the Middle East though could have come from the Caucuses.