hi,

see there is no specific engineering course available on satellite designing, a satellite designs course has various function which is closely related with aerospace engineering, mechanical engineering, computer science engineering, electrical and electronics engineering etc. you may have seen that in nasa or isro like organizations, many engineers or scientist works for a particular satellite when it was making to launch. so you may studying engineering courses related with this stream, then in future you may get works in those particular works providing organizations.

iist offers btech courses on following stream,

4-Year B.Tech. ( Aerospace Engineering )

4-Year B.Tech. (Electronics and Communication Engineering (Avionics))

5-Year Dual Degree (B.Tech. + Master of Science/Master of Technology

in 5 years dual degree course b.tech in engineering physics degree is awarded , also students may pursue the masters course topic in any of the  following stream,

Master of Science in Astronomy and Astrophysics

Master of Science in Solid State Physics

M.Tech. in Earth System Science

M.Tech. in Optical Engineering

however in 5 years integrated course there is no option for exit and quit the masters course, once you take admission in integrated course you must complete the 5 year course to get the degree certificate.

since you have interest in satellite design you should go for

4-Year B.Tech. ( Aerospace Engineering )

or

5-Year Dual Degree (B.Tech. + Master of Science/Master of Technology.