if you have a German child, you mostly have a legal right to get a residence permit after §188.8.131.52 Alien Law (Aufenthaltsgesetz). The Ausländerbehörde must check, if there are circumstances which block issuing this residence permit. For exaple a special amount of criminal record in the past. Im principle coming to Germany without papers and permission (which is the case for most people coming for asylum seeking) speaks agains issuing a residence permit, but if your reason to stay is a German child, the Ausländerbehörden mostly make an exclusion (this is possible after §39 Nr. 5 Aufenthaltsverordnung).
Anyway they must check it and give you a decision. If they decide to reject, they will normally first send you a warning letter and give you time for giving your opinion about it. In this case (or if they just give you a rejection), it is important to consult a good migrant councelling center or, better, a good lawyer with the expertise in alien law, very quickly. What can be done, depends then on the reasons.
But I hope that you will have a good scenario and just get your residence permit in some time.