I am active duty military new york non-resident, how do I file so it doesn't say I owe 1437$ in state tax?

If your income was military pay and you are stationed outside of NY and do not maintain housing in NY you are considered a non-resident and your income would not have been reportable to NY.  You would exclude your military income from the non-resident NY return.  This would result in a refund of any NY taxes withheld.  

If you filed a return that resulted in an amount due to NY, you will need to amend your return to exclude the military income.  Amendment forms are projected to be available in TurboTax mid to late March.  

You will simply select the "Amend" option at sign in and follow the prompts to make the changes.  You will need to print, sign and mail amendments in.