The best private colleges which offers admission to the course of BTech in CSE with the examination conducted by the institute itself is provided below-

MIT Manipal - Manipal Institute of Technology

VIT Vellore - Vellore Institute of Technology

SRM University Chennai - SRM Institute of Science and Technology

LPU Jalandhar - Lovely Professional University

Chandigarh University, Chandigarh

The fees of this colleges for the course ranges between Rs. 8lacs to 20 lacs for the entire 4 year course.

For more private engineering colleges consider the link below:

https://engineering.careers360.com/colleges/list-of-engineering-colleges-in-india?ownership=Private&branch=Computer%20Science%20Engineering

I hope this helps. Wish you a great eve!