Hi @Chubby
You do not need to withdraw your application for asylum. You can receive a residence permit under § 28 while your asylum case continues. This rule is based on paragraph 10 of the immigration law (Aufenthaltsgesetz) which covers such circumstances:
https://***.gesetze-im-internet.de/englisch_aufenthg/englisch_aufenthg.html#p0192
You’ll see in section 1 that it mentions additional requirements in cases other than where there is a legal entitlement. As you have correctly mentioned, the resident permit for a parent of a German child is an entitlement permit (in German ‚gesetzlicher Anspruch‘).
For the resident permit as a parent to a German child you do not require any level of German.
I do not see any reason why your application should need to take any longer so yes you can send them a reminder message. If for some reason there are additional questions on your application for § 28, you could for now make a separate application based on your current Aufenthaltsgestattung to move in with your girlfriend and child. This application is called ‚Änderung der Wohnsitzauflage‘ and is accepted to allow family members to live together. This would provide additional proof of your relationship with your child if necessary, although the fact that you have confirmation from the mother of how you are caring for your child then this is already sufficient.
Best,
Éanna