My JEE Main rank is 10359 from sc category. Which NIT college and branch can I get

You will not get any NIT with this rank

As per your rank and previous year cutoff, the colleges you get are:-

Mizoram University

IIIT Bhagalpur

IIIT Delhi

To know more about your chances of getting other colleges check out the college predictor link below:

https://engineering.careers360.com/jee-main-college-predictor

See, the possibility of getting the NIT will be based on the merit rank and that varies according to the college and branch. You may have many options to choose and one cannot accurately predict the college that you will e getting. But you will get the idea about the colleges in which you can get enrolled based on your marks and merit rank. Go through the link which provides you the cutoff marks for the various NITs branch wise so you can choose accurately the suitable NIT.

https://engineering.careers360.com/articles/jee-main-cutoff/amp#referrer=https%3A%2F%2Fwww.google.com&amp_tf=From%20%251%24s

Your jee mains rank and percentile is average enough to get an nit. You are not going to get nit trichy or nit warangal. You can get nit Durgapur mechanical, it. You can get similar branches in Andhra pradesh nit, Bhopal nit. You may get cse in nit sikkim, Mizoram, Manipur in the special rounds