https://www.marres.nl/EN/sarmatians.htm (This is a lengthy article giving the history of the Sarmatians...translation is a bit rough in parts)
citing Ammianus Marcellinus, the Poet Ausonius and others...
...After the death of the last Hun king Attila in 453, the vast majority of the Huns, who were composed of a multitude of ethnic groups retired to the Black Sea. In the late Sarmatian graves in that region Hunnic influences are found.
From the small groups Sarmatians who remained in Pannonia, is since little heard of. In 470 they fight against Ostrogoths. In 529 some of them go with the Lombards to Italy. They merge then in the Western European population. (27)...
Emperor Maiorinus 457-461 used Alanian and Sarmatian troops in battles against the Vandals in Africa and after the defeat they were disembarked in Gaul, where they will have been be recruited. They went looting presumably because of failure of payment and invaded thereafter for some time in northern Italy under King Beorgor.
In the Hungarian plain remained some Sarmatians after the Huns had gone. In the year 470 was their last known raid under their leader Babai when they again crossed the Danube and invaded Pannonia Secunda and conquered Singidunum (Belgrade).
The Eastern Roman emperor Leo I sent Theodoric a later Western Roman Emperor, to the Huns and he expelled them and killed Babai. In 568 followed some of the last Sarmatians of the Danube the Lombards and participated in the conquest of Italy and settled there in several colonies in the Po Valley.
No mention of a daughter of Babai....
