Game Design and Development

It is really tough to directly comment any institute best or not or answer which is the best institute in a city or country , especially for domains like animation and VFX or gaming where many institutes offer many types of courses for different duration for the almost all the same pipeline .
We need to see the content of the course , duration, cost , infra, earlier students outputs and skill developed , in-time course completion record , certification process & delivery of certificate in time etc.
Also Same Brand has different centers and branches and fortunately/unfortunately all does not perform the same . Some centers are doing great some not, in vary place to place centers to centers and also on the local management & team.
So its always good to visit the institute personally, speak to them, see the track record and then decide if its up to the mark as per your requirement.

It would be really helpful if you could have completed your 12th , Still give a try simultaneously if you have an option . Basically game development needed combination of 2 different skills like coding and programming knowledge and design knowledge with good grip on 3D modeling / texturing and lighting , map generation and baking .
Hence you must learn the basic coding and programming languages also must join some pre production course to learn the design principals and sketching & some 3D course to at least learn the CG asset creation part covering 3D modeling / texturing and lighting , map generation and baking.
This will help you to reach your goal.