Since this question is linked to your previous one, I will just post the link to it here:
To answer your question - how having a child with a residence-permit holder affects your situation - as I mentioned in the other thread, there are certain requirements that need to be fulfilled in order to receive a residence permit for Germany.
We have recently had a similar question on our platform that I've answered: https://www.wefugees.de/803053/how-can-get-residence-permit-for-germany-having-german-child
As you can read in that thread, when your child is German and you have proof of recognition of paternity, you would also need to have legal custody of your child in order to get a permit through your son (that applies to you as a non-EU citizen). Having claimed paternity doesn't give you 50% rights over the child, especially if the mother has sole custody.
Have you contacted the mother and talked to her about your wish to be part of his life?
On the link here, you should be able to find all different kinds of residence permits (on the right) and an explanation of all the requirements that need to be fulfilled.
Please let us know if you need any further assistance with your case.
All the best,