Firstly there are no BSc-MSc course in Computer Science Engineering. For Computer science engineering (CSE) you can go for dual degree BTech-MTech course in some of the colleges of South India provided below:

JNTUHCEH Hyderabad - JNTUH College of Engineering

IIIT Hyderabad - International Institute of Information Technology

RGUKT Basar - Rajiv Gandhi University of Knowledge Technologies

IIT Madras - Indian Institute of Technology

For more colleges you may visit the link provided below (you can click on the options in the left side in order to filter colleges based on your state):

https://engineering.careers360.com/colleges/list-of-dual-degree-in-computer-science-engineering-colleges-in-tamil-nadu

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