Living and working in NYC but work for a NJ company and NJ taxes (no NY taxes) are being taken out of check every week b. How do I file my taxes?

I have been working for a company that is located in New Jersey for the last four years and every year I want blow my brains out come tax time. I can never get the right answer. 

My employer taxes NJ taxes out of my check every week and no NY taxes. How do I file my taxes? This year I found an article stating if you work remotely you file your non resident return and put you earned $0 since you didn't earn any money there. By doing that you will get all the taxes you paid back in a refund, which sounds great. But what about NY? It shows I would owe NY close to $6300 for the year and I was only getting back $2,768. I am already in the hole for $6000 in taxes I owe NY for the same problem but I filed those return showing that I worked in NJ which I never did.

I keep getting different stories about how to file correctly. Please help!!!!!