As per the official notification, the eligibility criteria states:

A candidate must hold a degree of any of the Universities incorporated by an Act of the central or State Legislature in India or other educational institutions established by an Act of Parliament or declared to be deemed as a University under Section 3 of the University Grants Commission Act, 1956 or possess an equivalent qualification.

So yeah! the college you are studying at must be recognized by UGC.

For the official notification visit the link below:

https://upsc.gov.in/sites/default/files/Notice-CSP-2021-Engl-04032021N.pdf

To know more about UPSC 2021 visit the link below:

https://competition.careers360.com/exams/upsc-civil-services-exam

I hope this helps.