Hi aspirant,
Ofcourse there's is biotechnology for medical students. But, the main criteria for being eligible for this stream is that you should have studied maths in your high school i.e 11th and 12th while there are some institutions that do not take maths as a compulsion. All you have to have studied the subjects, physics, chemistry, biology or biotechnology.
Best Biotechnology lnstitutes are:
Delhi Technological University

National Institute of Technology

Anna University, Chennai

Birla Institute of Technology, Mesra

Vellore Institute of Technology (VIT), Tamilnadu

Institute of Chemical Technology, Mumbai

Good luck
Hope it helps