Hi @LuckyD
Has the father been legally resident in Germany for at least 8 years? If so, the child will have German citizenship and you are entitled to a residence permit as the parent of a German child.
Otherwise, the child will presumably be issued with a permit according to paragraph 33 of the Aufenthaltsgesetz. The only possibility for you to receive a permit in this situation is according to paragraph 36, section 2 of the Aufenthaltsgesetz. This law is for parents of foreign children who have a German residence permit. It is only issued in cases of extreme hardship (most commonly if the parent or child are in need of special care) and requires the livelihood of both to be secure (i.e. not receiving money form Sozialamt or Jobcenter).
Under section 25, which are permits for humanitarian reasons, there is the option of paragraph 25, section 5. This permit is given to people who have a Duldung for humanitarian reasons (e.g. because they have a child who is legally resident here). The person first has to have had a Duldung for 18 months before they can be issued with this kind of permit.
Best,
Éanna