Hi There,
Yes you can study psychology in part time but it may not be necessary that you'll be able to get M.Sc degree in that as it depends college to college. For example Andhra University: It offers M.A in psychology through distance learning ( https://www.andhrauniversity.edu.in/college/college-of-science-and-technology/science-departments/psychology-and-parapsychology )
Here is the list of the colleges that offers part time psychology courses:
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