Nope! There are no so called 'BTech Software Engineering' course in IIT's or NIT's. The MNC's such as the Google, Amazon, Whats app, Facebook etc recruits the BTech CSE graduates which is the course offered in both the IIT's and NITs. In general, all over India there are very few college which can offer such as course. See CSE is the most comprehensive course which you can get, to go for the Software Engineering, Web Development etc.

Some of the colleges providing the course of BTech Software Engineering:

SRM University Chennai - SRM Institute of Science and Technology

DTU Delhi - Delhi Technological University

Bharati Vidyapeeth Deemed University College of Engineering, Pune

School of Engineering and Technology, Jain University, Bangalore

For more colleges you may visit for Software Engineering BTech:

https://engineering.careers360.com/colleges/list-of-engineering-colleges-in-india?degree=B.E%20/B.Tech&branch=Software%20Engineering

To know more about CSE as a career visit the link below:

https://dqxeclau.top/courses/computer-science-engineering-course

To know more about Software Engineering as a career visit the link below:

https://dqxeclau.top/courses/software-engineering-course

I hope this answer helps. All the very best for your future endeavors!