Hello,
As you mentioned with SC category and 350 marks, your chances of getting a decent government college in your state through state quota(85%) are negligible as cutoffs are usually 370+.
However you might get some good private medical college in your state through state quota.
As the admission to medical colleges based on NEET is given under All India Quota(15%) and state quota(85%).
Average fees for private colleges may lie between 20-40 lakhs for whole course but it varies with each college.

However cutoffs change every year depending upon level of toughness of exam. So hope for the best and follow the counselling process.

Follow this link to better predict your college-
https://medicine.careers360.com/neet-college-predictor
Good luck

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