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 Thüringen
https://buerger.thueringen.de/portal/?PSTCATID=354234&SEARCHTYPE=PST&SOURCE=PstCategoryTree&tSt=1