YES, you are eligible for writing wbjee and getting admission in Jadavpur University, if you have a good rank.

(I, myself am from other state and studying in Jadavpur University. So, I think I am qualified to answer this question.)

Jadavpur University is a state-aided university  and as per the information brochure of wbjee(http://wbjeeb.nic.in/WebInfoExam... ), there is no requirement of domicile as long as candidate appears from general category to take admission in in such type of institutes.