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 Sachsen
Services for families: https://www.familie.sachsen.de/7425.html
Country Coordination Office for Single Parents Sachsen: http://www.shia-sachsen.de/landeskoordationsstelle-fuer-alleinerziehende-sachsen-.html
Foundation »Assistance for families, mother and child«: https://www.familie.sachsen.de/7450.html
Subsidy for family vacations and application offices: https://www.familie.sachsen.de/Familienurlaub.html and https://fs.egov.sachsen.de/formserv/findform?shortname=ksv_023&formtecid=2&areashortname=KSV&zbsbehoerde=103250
Association of single mothers and fathers e.V. Sachsen: http://www.sachsen.vamv.org/
Parent Network Dresden http://www.elternnetzwerk-dresden.de/das-netzwerk/alleinerziehende/wissenswertes-beratungsstellen.html