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 Hessen
General Information
http://www.familienatlas.de/alleinerziehend
http://www.kita.de/wissen/alleinerziehend/
http://www.familienatlas.de/geld/finanzielle-hilfen
Consultancy Guide: https://www.dajeb.de/beratungsfuehrer-online/beratung-in-ihrer-naehe/
Association of single mothers and fathers Hessen https://www.vamv-hessen.de/vamv-hessen-kontaktstellen/