I am on the 1st year of a TVöD E13 contract (offered for 2 years), and I would like to ask: what is the notice period for resigning from my current job?
If you are aiming for a fixed date and are still on good terms with your boss, it is quite common to create an "Aufhebungsvertrag", that is a contract in which you both agree to terminate your contract at a certain date, irrespective a of notice period. After all, you want to leave and your boss likely wants to hire someone new on your position.
You will likely get a call from the "Personalrat" though, as they want to check that you weren't somehow forced by your boss to contravene regulations this way.
I am also a postdoc in Germany on the same type of contract.
My contract states that within the probationary period, which is the first six months, the notice period is two weeks. Beyond that it says that the rules about notice period are defined in Section 30 paragraph 5 of the TVöD regulations. Googling for this leads me to this website (in German): https://www.der-oeffentliche-sektor.de/infoundrat/infothek/1483
Which, with the help of google translate, leads me to the conclusion that the notice period depends on how long you've been with your employer, counting not only your current contract but the whole continuous employment relationship if you were there before that. If you've been with them for 6 months - 1 year it would be four weeks. If 1-2 years then 6 weeks. 2-3 years -> 3 months. More than 3 years -> 4 months.