Dear @Georgii,
Welcome back to the Wefugees Community and sorry for the rather later reply.
Have you been to the immigration office already in the meantime? It is a bit difficult to predict what they are exactly planning (especially without knowing your situation well), but I assume that the immigration office might issue a Duldung ("temporary suspension of the deportation") for you. Do you have support by a lawyer in your case? I think it might not be that easy to eventually obtain the residence permit according to section 28 of the German Residence Act (as parent of a German child). Depending on the reaction of the immigration office now, I would definitely recommend to get some individual and confidential counselling. You did well though that you took care of the acknowledgment of the fatherhood and the declaration of custody already. Please don't hesitate to give us an update or to get back to us with any other question.
All the best,
Meike