In order to apply for a private medical college, state government will be doing the counselling. After that, if the seats are still vacant then the college can conduct its own counselling.

You have to register yourselves at various websites of each state government in which you want to apply after the results  

All the best 

For private colleges, there is no domicile required but you will have to apply separately as state & private colleges counseling will be conducted through particular state Govt authority.

Good Luck!!!