Here, I will add webpages that are useful for B.Sc/M.Sc students.
Visiting Students Research Program (VSRP) in TIFR Bombay https://mathweb.tifr.res.in/vsrp
Vigyan Vidushi program in Mathematics in TIFR Bombay https://mathweb.tifr.res.in/vigyanvidushi
Internship in CMI Chennai https://www.cmi.ac.in//admissions/internships.php
Summer Programme in Mathematics (SPIM) https://www.hri.res.in/academics/mathematics/math-vsp/
Long Term Visiting Students Program in ICTS Bangalore https://www.icts.res.in/academic/long-term-visiting-student-program