Game Design and Development

Sure, you can. After entering an IIT, you can take up any courses that you're interested in, there are tons of them. You can do minor engineering and minor projects on the same. Just find your interest and go for it.

Please mention the name of the institute for better assistance.

Why do you want to again opt for B.Sc Course after already completing graduation, infact you should opt for a Masters course in game design and development for better career prospects. You can pursue Masters Course from following institutes:
IACG
MAAC - India
Disney - India
Arena Multimedia
Indian School of Gaming.

Hello,
Kindly visit this link:
https://www.google.co.in/url?sa=t&source=web&rct=j&url=https://www.shiksha.com/b-tech/resources/jee-mains-college-predictor&ved=2ahUKEwjPs-iFqpTcAhWMRY8KHariB-kQFjAAegQIBBAB&usg=AOvVaw1N9BzFtyUCP4JU-2UQHQ0H

Check thelist of all Game Design Courses in colleges/institutes in India listed on Shiksha. Get all informationrelated to admissions, fees, courses, placements, reviews & more on Game Design Courses in colleges in India to help you decide which college you should be targeting for Game Design Courses in admissions in India. https://www.shiksha.com/design/communication-design/colleges/game-design-colleges-india.

Both are wonderful options and lots of opportunities are there in both these fields, but personally I have seen a lot of scope in game development in India. Packages will easily hit around 10-18 lacs per annum, for the post of senior game developer cum designer.

While some employers require a Bachelor's degree in video game design or computer Science, a high school Diploma is the minimum requirement. You may need to have experience working in computer Science, programming, or art. In addition, you need to be creative, have the ability to tell a story, and be able to work as part of a team. You also need to understand programming languages, software programs, and 3D modeling programs. You also need the ability to spend many work hours seated and looking at a computer monitor.

The total fees for the course is 75,000 and the duration is 6 months. For details, check the link below:
https://www.shiksha.com/it-software/game-design/course/diploma-in-mobile-game-development-s-a-g-e-school-of-advance-graphics-engineering-new-friends-colony-delhi-206822

Animations, BFX and other editing related applications, artistic work to. Be learnt.