You owe income tax to VA because that is where you live (on a Resident return). If you never set foot in NY, you do not owe NY tax. You will have to file a non-resident return, report zero taxable income, and claim a full refund. Expect NY to ask some questions. (And get your company to change your withholding.)
If you spend even one day of the year in NY, both states tax your income. NY taxes only your wages from the NY company (on a non-resident return) and VA taxes all your world-wide income (wages, plus investments, pension, or whatever else). VA will give you a partial credit for tax you paid to NY on the work income.
