Hi I came to US for 3 months on H1b and stayed in jersey city. But my employer in New york deducted New York state and city taxes assuming me to a staying in New York. My W2 also shows my home address to be office address which is from NY state. Please some tell me how to file tax even with wrong address on W2.

Where did you work?

New York city and lived in jersey city

Income earned in NY city must be reported on the NY state tax return. You should not be paying NY city taxes as you do not live in the city. Ask employer to stop withholding it.
Also report your income on NJ tax return. Claim credit for taxes paid to NJ. Your U.S. Tax Return: Working or Living in Two or More states