You should have mentioned your rank too. With 63.3 percentile score your general rank will be in the range of 385534 - 264383 and corresponding ST rank should be 15000 - 20000. You have less chance to get into NITs, IIITs or GFTIs with this rank. You should opt for private engineering colleges instead.

Following are some of the best private engineering colleges in India .

1. BITS Pilani
2. VIT Vellore
3. SRM University
4. KIIT
5. Thapar University
6. Manipal Institute of Technology
7. Lovely Professional University
8. Chandigarh University
9. RV College of Engineering
10. BITS Mesra
11. DA - IICT
12. KJ Somaiya College of Engineering

For more information regarding previous years' cutoff follow this link: https://engineering.careers360.com/articles/jee-main-cutoff-for-top-nits

However you have a chance to get a list of prescribed colleges against your rank. You just need to use JEE MAIN COLLEGE PREDICTOR. Click the link below, put necessary information and get result instantly.

https://engineering.careers360.com/jee-main-college-predictor?icn=QnA&ici=qna_answer

All the best.