You can get admission to IIT thru JEE Main and JEE Advanced. For NITs you can get admission thru DASA (Direct Admission Students Abroad) for stundents of NRIs and OCI card Holders. For that you need to pass SAT Subject in Mathematics, Physics and Chemistery. The Annual fee is USD8000. My son completed B.Tech like this. OCI cardholders can be resident of India and Studied in Indian schools.  However please check in JEE Main website OR NTA whether OCI card holders studied in India can get admission thru JEE Main. 4 years back it was not possible to join NITs thru JEE Main for OCI/PIO card holders.