Welcome to the Wefugees Community and thank you for reaching out to us.
I assume that you applied for asylum in Germany and the authorities opened a "Dublin" case as you were registered in another European country before you came here?
If you have a German child now, I recommend you to apply for a residence permit according to §28 of the residence law (which refers to family members of German citizens). It will be important that you are officially registered as father, which will include acknowledging the fatherhood ("Vaterschaftsanerkennung") and share the custody for the child ("Sorgerechtserklärung").
I hope this helps and please don't hesitate to get back to us with any further questions.
All the best,