No it is not necessary to have psychology in class 12th.

Eligibility Criteria (UG & PG) of Psychology

UG: Candidates must have passed 10+2 with at least 50% marks in aggregate. Independent entrance tests for UG programme are held by the various state, central and private universities.

PG: Candidates must hold a degree in Bachelor of Psychology along with a good score in entrance tests held for PG programme conducted by various state, central and private universities.

For more details get on the provided link--

https://www.careers360.com/courses/psychology-course#:~:text=Eligibility%20Criteria%20(UG%20%26%20PG),state%2C%20central%20and%20private%20universities.

For bethune college--

https://www.careers360.com/colleges/bethune-college-kolkata/bsc-psychology-hons-course