Students who are outsiders which don't have domicile certificate are eligible only for private colleges.

You can check below top colleges in WB through WBJEE

Jadavpur University, Kolkata

Heritage Institute of Technology, Kolkata

Institute of Engineering and Management, Kolkata

Maulana Abul Kalam Azad University of Technology, Kolkata

Haldia Institute of Technology, Haldia

To check the complete list you can refer below link

List of top engineering colleges through WBJEE 

To check the cut off you can refer below link

WBJEE Cut Off 

Good Luck!!