Game design

As far as I know, there is no degree required to work with a game studio, if you have one then it's a plus point but it's not important.
What you gotta do is show your work and experience.
Make your data structure and algorithms part strong and learn dynamic programming.

Hi Prince,
Here is the link to the best government colleges in India offering game designing:
https://www.univariety.com/search/india/top-animation-colleges
Feel free to raise more queries.
All the best.

You may take up any stream of your choice and then after completing 12th, you can take up a Bachelor degree in game designing.

Game design focuses on the creative vision for a game while game programming focuses on the technological methods of implementing the ideas of designers, using computer code to bring those games to life.
While there is little overlap between the two careers, they do go hand in hand. A game cant be created without both the designer and programmer working closely together from start to finish.

Both the courses are highly demanded these days. You may get into any of the courses. Game design will help you learn how a game application works and prepare a layout as per it. Whereas, animation will help you learn the tactics of animating anything in different modes.

B.Tech (animation and game design or cyber security and networking) would be the best.