I got 96 percentiles in jee main January. I am from obc category. Can I get nit or iiit

Ajay, you haven't mentioned the State and Category you belong to. This is important to know because the cut offs are different for Home State Candidates and Other State Candidates. So do please let us know your Home State and Category.

Meanwhile,your rank can be predicted by using the formula, (100-your total percentile)*869010/100. In your case, your approximate rank would be 34760. Let's say the number of candidates for April exam increased to 12,00,000 then your final rank shall be (100 - your total score) X 12,00,000/100.

With this rank, it might be difficult for NIT of your Home State even with OBC reservation. You might be able to get a good college through JOSAA. But if you want to appear for JEE Advanced, you qualify based on your percentile because the expected qualifying percentile is 85 and above. But if you want to study in NIT, you may have to appear in April session.
For IIIT Bangalore, your rank must be below 5000 and your score should be between 190-250.

Now to predict colleges, please use our college predictor:https://engineering.careers360.com/jee-main-college-predictor