Last week a brand new study was published on the genetic origin of the Hungarians. More closely they took a look at Hun, Avar, and Hungarian remains in the Carpathian basin.
I'm gonna just pick three points of the highlights:
- Genetic continuity is detected between Xiongnus and European Huns
- European Avars most likely originated from Mongolia and were related to Huns
- Conquering Hungarians had Ugric ancestry and later admixed with Sarmatians and Huns

First is important question to clear because their continuity wasn't obvious. The European Huns arrived here with different physical culture, with a strong Persian influence, they left behind their typical goods of the steppe people of the Scytho-Hunnic era. There is also some hundred years of hiatus between mentions of the Xiungnu in the east, and the appearance of the Huns in the western sources. It was just assumed that they are identical with the European Huns. As a Hungarian scholar put it: if a cat disappears under one side of the table, and appears on the other side, we can safely assume it is the same cat. The problem that this particular cat did not look entirely the same. Now we know, that genetically they were (perhaps in their language too, but culturally they had some differences).
So the Avars really were the Juan-Juans (or the Rouran Empire how the article writes it), which was just another state of the Huns apparently.
What isn't in the highlight about the Hungarians but found in the article: from the modern populations the closest genetically to those Hungarians who lived in the era of the Conquest of the Carpathian basin are the Bashkirs and Volga Tatars.
https://www.cell.com/current-biology/fulltext/S0960-9822(22)00732-1