Hii..

Yes of course you can take admission in government colleges in in West Bengal through  entrance exam. It does not matter if you have a Jharkhand domicile as it is not going to affect your admission. The present scenario in engineering colleges in such a way that almost 40 to 50% students in a batch are almost outside state students.

Thus you don't worry about domicile. 

Hope it helps. 

Best of luck