Alexonis is a Lithuanian name. The family probably comes from what is Lithuania today. Some chances are they came from a different part of the Russian empire as well.
It does not make much difference at this point, as no database of the kind you are asking for exists. Also, the name is of medium incidence and you may start to chase a wrong track even if you will find a similar name somewhere.

What you need, is to find more detailed information at "your side" about where from and when your ancestor did come in; and then look for a possible appropriate source at the "other side".