Hello aspirant, you have mentioned that your NEET 2020 rank is 35000 and you belong to ST category. According to these details, following are the colleges you can get a MBBS seat into -

1.Mysore Medical College And Research Institute

2.Government Medical College, Amritsar

3.Bangalore Medical College and Research Institute

4.Government Medical College, Kozhikode

5.Government Medical College, Surat

6.Government Medical College, Bhilwara

All the best