Hello,

There are many reputed and prestigious private and government engineering colleges in India that take admission through both JEE Main and JEE Advanced by their own counselling process which  are neither IIT nor NIT. Few of the many best colleges for engineering are:

1) BITS Pilani

2) Institute of Chemical Technology, Mumbai

3) Vellore Institute of Technology

4) Delhi Technological University

5) Jadavpur University

6) Indian Institute of Engineering Science and Technology, Shibpur

7) Motilal Nehru National Institute of Technology, Allahabad

8) Thapar Institute of Engineering & Technology

9) Netaji Subhash Institute of Technology

(10) BIT, Mesra

Please note that this is just a few of the many and I am not claiming them o be the top 10. List is wide and you may go through many more

https://engineering.careers360.com/colleges/ranking/top-government-engineering-colleges-in-India

https://engineering.careers360.com/colleges/ranking/top-private-engineering-colleges-in-India

Hello.

• BITS Pilani. Birla Institute of Technology and Sciences (BITS) Pilani is one of the top non-IITand NIT engineering college in India. ...
• Delhi Technological University. ...
• BITS Mesra. ...
• IIIT Hyderabad. ...
• Netaji Subhash Institute of Technology

• Anna University
• IIIT Allahabad
• Jadavpur University
• Colleges of Engineering Pune
• Punjab Engineering College

Hope this is helpful.

Good luck.