If you moved in 2020, you will file as a part year resident of both NY and NC. Assuming you don't meet the convenience of the employer rule, you will pay tax to NY on all your salary. You will pay tax to NC on the salary (and other income) earned after the move. NC will give you a credit, or partial credit for the tax you pay NY.
Once you are a full year NC resident (2021?), you will file a NY non resident return and pay tax to NY on all your NY based salary. You will also pay tax to NC on the salary . NC will give you a credit, or partial credit for the tax you pay NY.
