Asian Haplogroups in Europe is most likely reduced to 2 options.
The first is, they came during the Bronze Age Migrations from the Steppe.
Or, they came from the Huns, a Siberian/Mongoloid nomad people that arrived in Europe during the chaos of the late Roman Empire and the Barbarian invasions.
The Huns however, where a very short lived empire with little long lasting impact, much like the Mongols.