There are different state achievements You might be eligible for: separate maintenance/alimony, child benefit, parental benefits or housing benefit.
The cases are all treated individually, please contact the local authorities and counseling centers.
Information and consultation in Berlin
https://www.berlin.de/familie/de/informationen/alleinerziehende-getrennte-eltern-einelternfamilien-221
VAMV: Broschüre: Alleinerziehend – Tipps und Informationen
http://www.shia-berlin.de/