I am working in New York city but living in New Jersey. I am currently on OPT. So am I subject to the NYC Resident tax? Thanks a lot for answering!

No - only NYC residents are subject to NYC income tax. You do have to pay NY state non-resident income tax and NJ resident income tax. You will likely find that you end up owing NJ nothing since they give you a credit for taxes paid to NY State, but you still have to file with both states.