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 Saarland:
General information: http://www.familien-wegweiser.de/wegweiser/stichwortverzeichnis,did=93866.html
Caritas, consultation for single parent: http://www.caritas-merzig.de/66816.html
Booklet „Der Familienhelfer“: https://www.saarland.de/dokumente/res_soziales/Familien_mitEinlegeblatt_Aenderungen17.pdf