A master's degree in psychology is a graduate-level degree that generally involves two to three years of study beyond your undergraduate (bachelor's) degree. The two most common types of psychology master's degrees are the Master of Arts (M.A.) and the Master of Science.
Top Institutes offering M.Sc. Psychology are:

Allahabad University
Amity University
Awadhesh Pratap Singh University
BHU.
Hope this helps you.

Hello Sourav!

Here is a list of top colleges in India that have MSc in Psychology:-

Christ University, Bangalore

Presidency College, Chennai

Banaras Hindu University

University of Calcutta

University of Hyderabad

Pondicherry University

University of Allahabad

Loyola College of Social Sciences, Trivandrum

Hope this helps!
Good luck!