Welcome to the Wefugees Community and thank you for your question.
I assume that the immigration office (Ausländerbehörde) issued your son a residence permit according to section 33 of the German Residence Act - as child born in Germany with parents (or at least one parent) holding a residence permit. Please see the details on how to obtain this residence permit in Berlin, for instance, here. In general, a permanent residence (Niederlassungserlaubnis) is only given to adults or minors who are at least 16 years old. Please check this website for more information on this. Younger children's residence is usually dependent on their parents' residence permit in Germany. However, children born in Germany with parents who have stayed (legally) in Germany since at leat 8 years and who hold a permanent residence at the time of the birth may also be entitled to receive the German citizenship.
I hope this helps and please don't hesitate to get back to us with any further questions.
All the best,