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 Nordrhein-Westfalen
General Information
https://www.mkffi.nrw/der-staat-foerdert-familien-durch-finanzielle-leistungen
http://www.familie-in-nrw.de/2820.html
https://www.caritas.de/hilfeundberatung/ratgeber/familie/alleinerziehende/tipps
https://www.caritas.de/magazin/kampagne/familie/familienhelfen/ratundhilfe/alleinerziehend
Association of single mothers and fathers NRW https://www.vamv-nrw.de/ueber-uns/ortsverbaende/