It seems that aside from the notorious Chechen mercenaries who, aside from fighting Ukraine seem to have served as the enforcers among the various groups of irregular Russian mercenaries, there is now a battalion fighting for Ukraine.

https://www.facebook.com/kavkazbattalion/posts/1463379023929526

The Chechen Center is also worth following on Twitter.
https://twitter.com/ChechenCenter

I know there must be more to Chechnya than the pro-Russian mercenaries. In their war for separatism, between 75,000 and 250,000 civilians were killed. Despite the seeming control Russia has over them, they must be teeming with resentment.