Hii, 

If i see previous year cutoff trends,, then through 85% state quota counselling, the cutoff was 370 for getting into the government medical college, bettiah for sc candidate

And 371 for getting into Vardhaman institute of medical sciences, Pavapuri.

So your chances are pretty good to get into government medical, of Bihar through state quota counselling.

For more cut off details, you can visit below link

https://medicine.careers360.com/articles/neet-cutoff-bihar

Good luck!