Hello aspirant!
As far as the private medical college is concerned,the state govt does the counselling. After the counselling if still seats are vacant then the college starts to do its own counselling.
For applying you need to register yourself at each state governments website to enroll yourself in that counselling after the results.
Good luck to you!

Hi !

To apply for private medical colleges of nondomicile states , there is a simple procedure to follow. You just have to go to the official website of the respective state in which you wish to apply for the college , register for the counselling for the private colleges. After that , there will be display of merit lists , and according to your marks , you will be alloted a college. There is no need of domicile for registeration and counselling of private colleges.

Hope it helps !