As i understood about Attila the Hun was a conqueror but not successful on adapting farming life style. Those Turanic nations always been nomad and they were struggled adopting settled life. So my question is what really happened to Attila's heritage? are they assimilated or were they already minority over there and influenced by nations around them are they changed?
About the Hunnic-Hungarian relationship this answer by u/Ugocsa_non__coronat 's provides some relevant information.
However that answer does not mention a theory which was suggested by Sudár Balázs and other historians who are researching ancient Hungarian history. While Hunnic and Hungarian people are probably not related, one might make a case about the House of Árpád being the late descendants of Attila. While evidence apart from some murky tradition is nonexistent, we do know, that Nomadic emperors sometimes installed their descendants as rulers of other conquered nomadic people. About Attila we do know that he divided his empire between his sons, so it is plausible that one of his grandsons or great-grandsons later became a dynasty-founder among the former vassals of his empire.
Edit: I removed citations from the linked answer.
Edit2: I was being sloppy again. I have read up what Anonymus in Gesta Hungarorum - which might or might not use tradition as its primary source - exactly has to say on the topic to refresh my memory. According to him the House of Árpád is not directly descended from Attila, rather they have a common ancestor. So the dynasty founder would be not a son/grandson of the great emperor, but a brother/cousin/other unspecified relative.