@kuma_tw
This is known as a Claim of Right, under IRC 1341.
https://ttlc.intuit.com/turbotax-support/en-us/help-article/taxation/claim-right-repayment/L0aW5v3Tp...
Essentially, you were paid a salary in the past that you paid taxes on, that you believed at the time you had a right to the money. If the amount you paid back is less than $3000 there is no tax relief. If the amount is more than $3000, you can use the Claim of Right procedure.
Federal tax return
You have two options. Instructions are linked above.
1. Take a tax deduction for the amount you repaid.
2. Claim a tax credit for the amount of income tax you overpaid in the previous year. You have to figure the amount of the credit yourself. Look at the year you got the bonus, and figure your taxes with the bonus, and figure them again as if you did not get the bonus. That is the amount of credit you can claim in the year of repayment. To claim the credit, you must use Turbotax Desktop version installed on your own Mac or PC from a download, you can't claim the credit online.
Two notes: If you already itemize your deductions, and if your tax situation is very similar to the year you were paid the bonus, then the simple deduction will come out about the same as the credit, and is easier to claim, and can be done with Turbotax online. You are allowed to use whichever method results in the largest benefit, so you may want to figure it out both ways.
Also, you can only use the tax credit method if you believed at the time you got the bonus that you had an unrestricted right to that income. If you knew when you accepted the bonus that you did not have a right to it, you can only use the deduction method. (For example, if you were planning all along to leave the company before you worked there long enough to get past the repayment requirement, then you did not have an unrestricted right to the bonus.)
State income taxes
Look on your state tax return instructions for how to make a claim of right credit. Every state is different. When you get to the specific process of filing your return, you can try calling customer support or posting here to ask a state expert if you can't find it.
Social security and Medicare tax
You can claim a refund of social security and medicare using form 843. This form is not included in Turbotax and is not filed with your tax return, you prepare and file it separately. Include a statement and any documentation showing that the company refused to adjust your withholding or provide a refund, if you can get such a statement. Instructions are here.
https://www.irs.gov/forms-pubs/about-form-843
