Hello.
There is no branch like mechatronics in NIT so so you will not what get any NIT for this branch and for more detail about some of the best colleges and university in India which offer mechatronics branch, you can refer below link, here you can compare these universities or colleges with their rating.
https://engineering.careers360.com/colleges/list-of-mechatronics-engineering-colleges-in-india
Best of luck.