I live in Florida and my job in North Carolina withheld state taxes. How do I amend state tax and will the taxes withheld be refunded?

You don't amend your income tax return. You'll file a nonresident NC state income tax return. 

• Yes, NC should refund the state income taxes withheld in error by your employer. 

Since payroll departments aren't always aware of how withholding works, remote employers sometimes withhold taxes for their state, not the employee's state.

• In these cases, you need to file a nonresident return to recover the erroneous withholdings. On the nonresident return, declare earnings of $0 so you can get a full refund for the taxes your employer withheld. You should also tell your payroll department so they fix this in the future.

For instructions on how to file a NC nonresident state income tax return, please see How do I file a nonresident state return?

Thank you for the quick response. What if I've already filled for 2022, and returns were already processed? Then would I amend, what's the next steps for me to get the refund?

If you have already filed a North Carolina non-resident return and neglected to include your withholding, then yes, you will need to amend your NC return.  However, if you never filed a NC return, then there is nothing to amend.  Instead, as @HelenC12 suggests, file a non-resident NC return and include your withholding.  

From your post, it appears you have already filed your returns and those returns have been accepted.  Thus, you are now ready to amend. Therefore, you can access your previously filed return, in TurboTax online, from the TurboTax home page.  Scroll down the screen to the section Your tax return & documents.  Click on the drop-down arrow and select Amend (change) 2022 return.  If you used TurboTax CD/download, then you can amend your previously filed return by selecting Other Tax Situations, and then scroll down to Other Tax Forms. 

@jarrod-cribbs