Domicile is only require for getting the government seats.Other state candidate not able to fetch government seat without a domicile.In your case as you belong to other state you are only eligible for private colleges of west bengal.Any candidate who is resident of India can write the exam.

To get good private colleges you should require very good rank .

To know more about WBJEE follow this link:https://engineering.careers360.com/articles/wbjee-eligibility-criteria

To know more about WBJEE CUTOFFS follow this link:https://engineering.careers360.com/articles/wbjee-cutoff