Hello Aspirant, 
Bsc Psychology is a 3 year degree course and basic eligibility criteria for this course is that you should have passed your 10+2 with minimum 50% from a renowned board in science stream. Even if you dont have psychology as your subject in 10+2 then its okay, you can still pursue your Bsc in psychology.

In Kolkata the following institutes include Bsc psychology,
Asutosh College,
Bethune College,
Gokhale Memorial girls college,
Kingston College,
St.Xaviers College,
Calcutta University.
These are the some of the good colleges in Kolkata which provides Bsc in psychology.
The admission process is direct and some may conduct entrance. You can go to the college official website for any information realted to the college.
Hope that answers your question.
Further doubts can be asked in the comments section.
Thank you.