I have been working as a software engineer part-time/werkstudent for the past one year. I had 'employer A' for the first 2 months of the past year. When I quit employer A in order to join employer B, I had holidays remaining from employer A.

Employer A refused to grant me my holidays and insisted that I get the holiday as money.

I legally left Employer A in month 2 and joined Employer B in the start of month 3. However, Employer A submitted to the tax office that I worked one week in month 3 (even though I didn't) and sent me my 'holiday payout' as 'salary' as if I worked for them ( i don't know if this is normal, because i am new in germany -- is this how holiday payouts work here? ).

I asked Employer A and they said this is the correct way to pay out vacation days.

According to the tax office, I assume, I worked parallely for both Employer A and Employer B in week 1 of month 3.

In my payslips from Employer A, my Tax Class was 1 for the first 2 months. The last payslip ( 'holiday payout' ) has my Tax Class set as 6.

I just realised that all payslips from Employer B also has my Tax Class set as 6, which is incorrect because I never worked for two employers at the same time. Now, I need to submit my tax return to apply for tax refund but I do not know what to do with this wrong tax class information in my payslips.

TLDR: I never ever worked for two employers at the same time but I've been paying taxes under tax class 6. It was probably due to the fault of my first employer. Now I have to file my tax returns and I do not know what to do.