Hello acharya,

As per my knowledge you should take up cse rather than it because I haven't heard much about universities which provides p.hd in information technology but in cse you would get a huge amount of colleges /universities.

Here is some of the colleges which provides p.hd:-

1-IIT Bombay - Indian Institute of Technology

2-COEP Pune - College of Engineering

3-ICT Mumbai - Institute of Chemical Technology

4-VJTI Mumbai - Veermata Jijabai Technological Institute

5-RVCE Bangalore - RV College of Engineering

6-IIT Madras - Indian Institute of Technology

For more information you can check out the link given below-

https://engineering.careers360.com/colleges/list-of-phd-in-computer-science-engineering-colleges-in-india