Thank you for sharing your situation with the Wefugees Community and sorry for the rather late reply.
In order to assess your case a bit closer, some details will be important.
For example, are you living together with mother and child? Have you declared the custody for the child ("Sorgerechtserklärung") and are you officially listed as the father in the child's birth certificate?
It could also help to know, if you or the child's mother are working.
I am sure, that one of our experts, as @mbeon-Christine or @manrhei-mbeon are very happy to give you some advice then.
Looking forward to hear from you again.
All the best,