Welcome back to the Wefugees Community and thank you for reaching out to us again.
I saw that you opened a second thread with the same content. In order to keep a better overview and information in one place, I closed that one. I hope you understand.
We discussed a very similar situation already here. I think my explanations may correspond to your questions as well as I wrote:
Regarding the requirements for the residence permit according to §28 (1) No. 3 (as parent of a German child), it is not absolutely necessary to be registered at the same address as your child. Instead, the authorities will more likely check if you share the custody for the child. You need to prove that you have a parent-child relation and you are actually taking care of and see the child regularly. The law calls this "familiäre Lebensgemeinschaft". Another relevant aspect is the financial child support. In case you face difficulties in finding agreements regarding seeing the child etc., you may ask the local "Jugendamt" for support as well. They are always aiming at acting in the child's best interest and could play a mediating role between you and your child's mother. In the worst case and if you both can not find any solution, you may need to take the case to court. However, I really hope that you can find good ways of communication and common sense - especially regarding the benefit and well-being of your child.
However, I will also link our dear @mbeon-fardeen - am I correct on this and/or is there anything you would like to add?
In any case, don't hesitate to get back to us (if it's related to the same question, preferably in this thread) with any further questions.
All the best,