Dear Candidate

Yes, most certainly you should be able to quality NEET 2018 with 113 marks under ST category. This mark appears to be in a safe zone when we consider the qualifying marks of last year. In NEET 2017, for ST category candidates, the qualifying marks was 107 (of 720). 

MCI will give NOC to all candidates who qualify NEET 2018, assuming that you are asking this in context of going abroad for MBBS studies. 

Hope it answers. 

All the best!