There are various colleges that offers part time PhD in psychology in India. These are given below:
1. Amity University
2. Lovely professional University
3. Jamia millia Islamia
4. Nehru group of institutions
5. Acharya Nagarjuna University

To get admission in these colleges you can visit the official webistes or you can contact them.
Below I am attaching a link for your reference
https://university.careers360.com/colleges/list-of-phd-in-psychology-universities-in-india

Hope this helps