Welcome back to the Wefugees Community - I am really sorry to hear that you couldn't solve these issues yet. I remember from your last questions that the case went already to court, right? Could you get any clarification about the outcome by now? As I mentioned also in your earlier opened threads - unfortunately, I am not an expert on family law. But the father should assume responsibility and at the end the authorities usually have an interest in knowing your child's father as well - latest when you apply for "Unterhaltsvorschuss" (as we discussed, for instance, here). I recommend you to contact a counselling office to get some individual support (you may use this search engine or share with us your approximate location, so we can help you with the research).
At the end, your child will not obtain the German citizenship as child of a German father if he is not officially the father (as written in the birth certificate). Subsequently, you could not apply for a residence permit according to section 28 of the German Residence Act as mother of a German child. At the end, it is necessary to assess your personal situation and your options with an expert either with a lawyer or in a counselling office.
In any case, please also don't hesiate to get back to us and to keep us updated.
All the best,