Welcome to the Wefugees community and thank you for reaching out to us!
The reason why the Landratsamt asked you to wait for the outcome of your asylum procedure is because you need a legal status in order to receive a residence permit. You would have to wait how the appeal process goes and what title you will have after. If you are granted a residence title (refugee protection, asylum), you will automatically get a residence permit.
If your appeal is denied and your asylum claim is rejected, you still have the chance to receive a residence title through your child. It plays a role if you acknowledged paternity (Vaterschaftsanerkennung) and have shared legal custody of your child with the mother.
In case your appeal is rejected, here is a very helpful website by Flüchtlingsrat Niedersachsen on "9 perspectives after a negative decision on your asylum case" (it's in German, but translation programs help :-) :
Since I am not a lawyer, I highly advise you to seek support from a legal aid service or consult a lawyer regarding your situation, to see whether or not you should withdraw your appeal now.
Here is a list of German pro bono legal aid services: http://www.refugeelegalaidinformation.org/germany-pro-bono-directory
Please also have a look at these threads from our platform that discuss how to get a residence permit through having a child:
How to get a Meldebestätigung in order to apply for a residence permit?
How can I get a residence permit for Germany having a German child?
Advice on getting residency permit for Germany
I hope this information helps. Feel free to reach out to us again if you need any further assistance!