Hello,
It's fine to having the qualification and you can take an admission in private college through UPSEE counselling by which you get a low fee structure. If you can say your rank then that would be more helpfull to suggest you some names. YOU can look for it.

AS per JEE, it will be difficult but yes you can get an admission in any private college in your domicile or state unversity. YOU have to apply for counselling. You may get by state quota and your jee percentile. it is difficult but may be possible. Anyway , you have to search for some and try for it.

you can use the UPSEE college predictor to get the list:- https://www.careers360.com/upsee-college-predictor

Hope it helps!