Greetings!

The truth needs to be told and the truth is that you are NOT eligible for IIT/NIT. The criteria for NITs/IITs for ST category is that you must have greater than 65% in your board examination, or you must be in top 20 percentile in boards( which if you have less than 65 % is highly unlikely).

This leaves you with two options, one is to take a drop and first appear for improvement exam in boards and then again appear for JEE in next year and take admission in college according to that percentile.

The second option is to look for private colleges that don't have such criteria or who have more liberal criteria for boards, for that you can use the following predictor

https://engineering.careers360.com/jee-advanced-college-predictor?utm_source=qna&utm_medium=jee_adv_cp