I started a second employment in November 2019, with a monthly pay below 450 Euros, and I don't have any other second employments. I'm now doing my tax declarations, and I have just realized that all this time, the employer actually classified the job under Steuerklasse 6 instead of Minijob! If this goes unchanged, I'll not only not get the full pay, but I'll have to pay a huge amount of Nachzahlung (> 1500 Euros) to the Finanzamt, due to Steuerklasse 6 being taxed really harshly.
I know that I'm a total idiot for not realizing the issue for so long. I just assumed that the employer would do its job and classify the employment correctly. I didn't even know that it was still possible for a job below 450 Euros to be technically classified into one of the Steuerklassen. And whenever I received the pay at the end of the month, I just thought the Pauschal amount was deducted from it. I didn't even look into the issue when I received the Lohnsteuerbescheinigung earlier this year, thinking that since it was another employment after all, it would be natural for me to receive such a document, even though it should have been a Minijob. Only now that I go through a Steuererklärung software, did this issue dawn on me, and I realized what Steuerklasse 6 really means after doing a search online.
Can I still do something about it? From what I saw somewhere around the web, e.g.
https://www.datev-community.de/t5/Personalwirtschaft/Minijob-r%C3%BCckwirkende-%C3%84nderung-Steuermerkmal/td-p/183948#_=_ and https://www.haufe.de/personal/haufe-personal-office-platin/minijob-geringfuegig-entlohnte-beschaeftigungen-in-der-en-332-wechsel-nach-ablauf-des-kalenderjahres_idesk_PI42323_HI2812335.html, it's apparently possible to retroactively say that the job should be treated as a Minijob, as long as it is communicated to and discussed with the Minijobzentrum and the Finanzamt. I guess I'll need to contact the employer and tell them to do so as soon as possible?
If for some reason the past tax classification cannot be changed anymore, is there any benefit for me at all for the job to be classified under Steuerklasse 6 instead of under Minijob? From what I see, there seem to be pure disadvantages (since even for a Minijob the employer still pays into Rentenversicherung anyways), and I can't believe the current situation is actually something possible.