I have scored 362 marks in neet 2020, can i get any private collage, in obc category from bihar.

Hello sir, yess you can get a college since you qualified the eligibility criteria. Ofcourse government is not an option but you can get a seat in private college. Also you'll get a good college as cutoff for your category is comparatively low. I'll give you a link below of all the private colleges, but also I would recommend you college predictor to get you perfect college as per your marks.
College predictor - https://medicine.careers360.com/neet-college-predictor?icn=QnA&ici=qna_answer
List of private medical colleges is india - https://medicine.careers360.com/colleges/list-of-private-medical-colleges-in-india
I hope this helps
Thankyou.