No IIST don't offer BSc Astrophysics/Astronomy course. Although the institute offers MS Astronomy and Astrophysics which a student can pursue by qualifying GATE examination after a MSc Physics/BTech degree which you can see by visiting the official website.

The courses offered in the UG level on the basis of JEE Advanced are:

B.Tech Aerospace Engineering

B.Tech Avionics

B.Tech Engineering Physics Dual Degree

To know more about IIST you may visit the link below:

https://www.careers360.com/university/indian-institute-of-space-science-and-technology-thiruvananthapuram

For official website visit the link below:

https://www.iist.ac.in/

To know more about Astrophysics visit the link below:

https://www.careers360.com/courses/astrophysics-course

I hope this answer helps. All the very best for your future endeavors!