No States accept other State domicile candidates for their Private Medical College seats for Government Quota. But there is no such rule for Management Quota. Anyone can apply for Management Seats. The domicile rules dont apply to Management Quota seats. But please remember that rhe fees is usually too high. And if the seats in State Counselling lie vacant, then the authorities will turn over the seats to the collehes and then the colleges can decide how to conduct admissions for such seats.

Uptill this year, only government medical colleges have seats allotted for all India quota.so there are no seats in private medical college.
The below article from Times of India says that it will be implemented this year on but the FAQs section on the main website mcc.nic.in does not talk about it so we can't say for sure if it's implemented. So until the official website reflects changes we can say that private medical colleges don't have AIQ seats.
https://www.google.com/amp/s/m.timesofindia.com/home/education/news/15-seats-to-be-reserved-for-all-india-students-in-private-medical-colleges-from-this-year/amp_articleshow/69756415.cms