No, you are not allowed to work with Zenjob if you receive social benefits (Sozialleistungen).
This refers to the social benefits (Arbeitslosengeld I) according to the Third Social Code (Drittes Gesetzbuch) and the unemployment benefits II (Arbeitslosengeld II, also called "Bürgergeld") according to the Second Social Code (Zweites Sozialgesetzbuch).
Child benefit and BAföG are excluded from this regulation.
Why is that? The legislator otherwise assumes that a professional status exists. This is not possible in a short-term employment in which you are employed at Zenjob.
If you have any further questions on this topic, click Submit a Request.