Wrong State Taxes Withheld

I live in VA.  When I started a new job in February 2022, they took out both VA and NY taxes (headquarters is in NY, but my location was in VA).  I noticed it after a month, but they took out $95 for NY by then.  How do I get the NY state tax refunded though?  My W-2 shows both VA and NY taxes withheld, but TurboTax says it doesn't think I need to file a NY tax return.  No matter what I try, it keeps saying I owe thousands to NY.  Any help is greatly appreciated!