The problem you will have is that New York wages were entered on your W-2, as evidenced by the abbreviation "NY" in box 15 and wages listed in box 16? Consequently, New York is going to assume you earned income there and it will be difficult to convince them otherwise. Your best option is to get a corrected W-2 issued showing no New York wages.
New York can tax you on work you do remotely for a New York based company, but only if you are working remotely out of convenience, not out of necessity. In other words, if the company in New York that you work for has a facility there that you could preform your services at, then they can under the tax laws of New York tax you on your earnings from that company.
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