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 Baden-Württemberg:
General information: https://www.service-bw.de/web/guest/lebenslage/-/lebenslage/Alleinerziehende-5001124-lebenslage-0?tab=0
Caritas: https://www.caritas.de/hilfeundberatung/ratgeber/familie/alleinerziehende/tipps
Youth Offices Baden-Württemberg: https://www.kinderinfo.de/jugendaemter/baden-wuerttemberg/