Private Medical Colleges do not participate in All India Counselling and the seats are filled through State Counselling alone. And for appearing for State Counselling you need to hold the domicile of that particular State. Or else the only other option is through Management Quota. Under All India Quota, All the 15% of All India Quota Seats except for Jammu and Kashmir, 100% Seats at Deemed and Central Universities, IP Quota seats in ESIC Colleges, Seats at AFMC are filled by DGHS. The 85% State Quota and Private Colleges are filled by the respective State Authorities. And there are 3 Categories in Private Medical Colleges. Category A is the Government Quota Seats. And only candidates of the home State are eligible to apply for these seats. B Category seats are also called Management Quota Seats and they are filled through State Counseling and the remaining seats are filled through direct Admissions by contacting the College directly. Here the fees is usually nothing less than 40 lakhs. The last Category is NRI seats Category and you cannot apply for that. So to just answer your question, you will have to wait until all the rounds of counselling are over to try for a seat in a Private Medical College for lower NEET score. There will always be Medical Colleges which will have few seats left unfilled. But as mentioned, their fees will be between 30-40 lakhs.