I consider you are asking about the BTech/BE course in Civil Engineering. I am listing here some of the government colleges for BTech/BE civil Engineer:

IIT Bombay - Indian Institute of Technology

COEP Pune - College of Engineering

IIT Madras - Indian Institute of Technology

MSU Baroda - Maharaja Sayajirao University of Baroda

DTU Delhi - Delhi Technological University

JMI New Delhi - Jamia Millia Islamia

LDCE Ahmedabad - LD College of Engineering

For more colleges (Government) you may visit the link below:

https://engineering.careers360.com/colleges/list-of-engineering-colleges-in-india?ownership=Public/Government&branch=Civil%20Engineering

To know more about the career in Civil Engineering visit the link below:

https://www.careers360.com/courses/civil-engineering-course

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