Guys, I am a dropper and just want CSE in some reputed college, what exams should I give?

I am obviously giving JEE mains (and advanced hopefully). I also want to give other exams than mains for other colleges, as I am a dropper who barely qualified for advanced last year. But the alternative exams should be not more than two, as I live in a small town and travelling different cities for exams won't be easy.

Few questions:

What two different exams should I give? (Before recommending me state govt exams, consider that I live in punjab).

Can we get admission in VIT and MIT on the basis of Jee mains? If yes then is there any benefit of attempting their exams?

NOTE: I have already decided my branch as CSE, as coding is my passion, I took engineering only because of that. So, I would not prefer sacrificing branches for getting better colleges.