Welcome back to the Wefugees Community and thank you for reaching out to us.
I assume you saw the answer in the last thread you opened, right?Our expert mbeon-Bernd is giving many useful information on that topic here already.
However, please also see this website for more information on the required documents for the "Vaterschaftsanerkennung" (acknowledgement of the fatherhood). As far as I can see, a registration document or "Meldebescheinigung" is not needed.
The fact, that the German authorities have different data than your passport is showing, can of course lead to issues in various aspects in the future. I am afraid that you need to contact a lawyer in that case.
All the best,