Game design

Only through self learning and practice, you can become a game designer in India as most of the courses that are available either teaches you how to become a game artist or game programmer but never a game designer, even the courses that says Game Design on its title, focuses heavily on game art side of things and little on game design.
Game design is a vast subject so my suggestion to you would be to read books or watch tutorials on game design, play games not to enjoy but to deconstruct and understand them and most importantly try making some games yourself.

Hello Vipin,
These days a large number of engineers are unemployed. Hence it's essential that one must think of those courses which will give better chances of employment. I feel that B.Sc with computers and game designing or web designing will get you job. Go ahead.

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.