Hello Aniket, 

This a list of some of the best psychology colleges in India you can apply to: 

1. Christ University,  Bangalore

2. Presidency University,  Kolkata

3. Ferguson College, Pune

4. K. J. Somaiya College of Arts and Commerce, Mumbai

5. Jesus and Mary College, New Delhi

6. Jai Hind college, Mumbai

7. St. Xavier's

8. St. Andrew's College of Arts, Science and Commerce

9. MCASC, Sivajinagar

10. KC college, Mumbai

Here are some colleges in Bihar that provide this degree: 

1. Patna University

2. Amity University

3. Bihar National College

4. Gaya College

5. T.N.B college,  Bhagalpur

6. Matildhari College

All the best! 

Hope this helps :)