A new preprint, Mitogenomic data indicate admixture components of Asian Hun and Srubnaya origin in the Hungarian Conquerors, throws a rather large sample of medieval mtDNA samples at the question of the ethnogenesis of the Magyar people. The context here is that Maygars speak a non-Indo-European language, with a distant relationship to the Finnic ones, but genetically are not much distinguished from their neighbors.
But the differences are not non-zero, ‘best of breed’ methods can pick up a small fraction of exotic ancestry.
The results above are based on samples from cemeteries of the Magyar elite. These are people who identified with a steppe confederacy which coalesced in the 9th century in the Volga region, and in 895 conquered the region of Central Europe which we now term Hungary. In the 10th century, the Magyar tribes were an alien and predatory force within Europe, pagan and exotic. They were, in fact, the latest in a long time of mobile Central Asian horsemen, going back to the Scythian, Sarmatians, Huns, and Avars.
What the data from these results confirm is that a substantial proportion of the maternal lineages of the Hungarian nobility were East Eurasian. Their genetic profiles, in fact, resembled Scythians who had mixed with Altaic peoples, even if they were not descended from those people. What this suggests is that the Magyar conquest elite was part of a broader landscape of ethnolinguistically distinct, but interconnected, steppe confederations. The preprint gives great space to the likelihood that a substantial proportion of the Magyar elite was in fact Turkic in origin.
This leads to one of the major assertions of the paper: the distinctive linguistic identity of modern Hungarians is a legacy of the Hunnic period, and not the Magyar conquest. From what I can tell they didn’t have older DNA, so I don’t know how they came to this conclusion, except that the conquest Magyars were small in number, and seem to have been decimated over time (Mongol invasion, the battle of Mohacs).