Why can’t you take the letter to HR yourself? You can also, scan a signed letter, an email it to HR. However, if they will backdate your notice period, is entirely up to your HR department. You probably should have hand delivered the letter yourself or at least emailed a copy for the initial notification

When you sent the letter doesn't matter per se, what matters is when they have “access” to it (the German word is zugehen). I don't know what that means precisely and I am not a lawyer but if they are notified late on Feb 28 or if the letter is not available for pick-up until the next day then it's possible that they would not be considered to have had access to it before March 1st. On the other hand, if they refuse to collect it then that's on them but that's not the issue it seems.

Did you talk to them on Friday to let them know it was coming? Have you tried to negotiate the notice period? Do they have any reason to make difficulties? Have you got another job lined up? In Germany or elsewhere? Can you afford to burn some bridges? Ultimately, there is not much point dwelling on whether it's your fault or if you made a mistake, that doesn't really matter legally and practically. Instead, consider your options and priorities.

Do you really have to work untill the end of third month? Here (Croatia) it would be 3 months, which would be same date 3 months from now, and difference would be between end of May and beginning of July, not whole month

I really don't know why this has 4 downvotes. I edited it a little for clarity, but it is an interesting and practical question that an HR professional could know.

@Deepika: what is your exact proof of delivery and signature and what's the date on it?

I don't know about i Germany, but in the UK, email legall counts as in writing

In Germany mostly it's always in Writing.

I don't know about Germany but I would normally expect your letter to clearly state the date of your resignation "As from 22nd March 2022 I resign my position as ..." and any required notice period to run from the date the company was notified to collect it, not the date it landed on someone's desk. Finally it seems a crazy situation that a one day delay can cost you a month, are you sure about that??

The first Google result by a law firm says it does not count as delivered when it went to the postal office and specifically recommends not using registered mail because you might miss the deadline.

This is a law question, not specific to employment.

effective immediately as of @Alan +1. The part I don't get is the company putting themselves on the hook to pay them for all of March, when they shouldn't be letting the OP inside the building anymore regardless.

Great point @Mazura

Can I borrow your pen, sir?

@Mazura yes that's correct but I have got to know from my ex-colleagues that HR is always like this and some have served 4 months notice period because the negotiation could not be mutually agreed with the employee-manager(especially manager wants to get the work done as much as possible even more than 3 months)

The "stupid kindergarden game" exists where I live. I'm not sure what to call that other than a very specific profanity.

“ The end date for resigning in March compared to February will be one month longer, since the notice period starts the month after my official resignation.” Huh? Are you saying that if you gave notice on March 1st, you would have to continue working for two months but if you give notice on March 31st, you would only have to continue for 1 month?

@AffableAmbler yes. If I give notice on March 1st or March 31st end date would be June end..

First, it depends on the specific wording of your contract, and 2) that makes it a legal question. You would be better off asking this at law.stackexchange.com.