According to the previous year cutoff which I have find your chances of getting private/ government Medical Colleges under schedule caste category is very low or almost nil. I am mentioning below the name of the colleges along with their required cutoff score of previous years. These cutoffs are under 85% quota.:

1. Anurag Narayan Magadh Medical College and Hospital of Gaya 420
2. Darbhanga Medical College 438
3. Government Medical College bettiah 414
4. Indira Gandhi Institute of Medical Sciences Patna 463
5. Jawaharlal Nehru Medical College Bhagalpur 430
6. Nalanda Medical College Patna 451
7. Shri Krishna Medical College and Hospital Muzaffarnagar 426
8. Vardhman Institute of Medical Sciences 419
9. Patna Medical College Patna 481

However the cutoffs of colleges changes every year and, you may get chance to get government seat.

Read More about Bihar cutoff by clicking on mentioned below link:

https://www.google.com/url?sa=t&source=web&rct=j&url=https://medicine.careers360.com/articles/neet-cutoff-bihar/amp&ved=2ahUKEwiVp-PJh7P1AhXOdd4KHTpqAAkQFnoECCwQAQ&usg=AOvVaw1U6-vyKjpN-TmR5bUm3NYf