...

[th20221]

...

[DavidD66]

Don't confuse "taxed" and withholding.  Even though South Carolina tax wasn't withheld, as a resident all of your income is taxed by South Carolina.  You should enter the total amount you earned from the New York company as the amount that was taxed by both NY and SC.  To prevent double taxation, South Carolina will give you a credit for tax paid to New York. 

[th20221]

...

[DMarkM1]

Yes.  You will enter the entire amount taxed by NY.  Your resident state (SC) on your tax return will be taxing all income from all sources even if nothing was withheld on your W2.  Therefore the NY income will be double taxed on your returns.  To mitigate that double taxation you will claim the credit for taxes paid to another state on your resident (SC) return.