Hi, You can apply for WBJEE and get into good colleges in West Bengal then there is no requirement to go in UP colleges until you have interest in specific college in UP.
The eligibility states:
Aspirants of WBJEE should be residents of West Bengal for 10 years consecutively, as on December 31, year of admission.
You can also check the complete criteria here to apply in WB: WBJEE Eligibility Criteria

Also to apply in other states you will have to give JEE MAIN. Now this year onwards this is the centralised exam for all state admissions.

Hope this helps. Good Luck!