If you are interested in BCA then you don't need to appear for JEE Main or UPTU because these exams are not for BCA, It is for B.tech Programmes. there is no any common entrance exam for BCA. Each University has different criteria to take the admission some university takes the admission on the basis of Merit list & some takes the entrance.

If you want to go for only Gov. colleges for BCA then you can prefer the colleges:

University Lucknow

Bundelkhand University

Admission is based on the merit obtained by the candidate in the entrance test conducted by the Universities.

Good Luck!