In Zammad SaaS you can get a whole backup (of all data) twice per year free of charge. There is no backup function for specific customer tickets etc at all.
If you need that, you can create API scripts that provide that kind of functionality.
It doesn’t matter if self hosted or not.
This post might be of interest to you. Do note that this is an exporter for archival purposes, not a true backup solution. You cannot import the data back into Zammad with this tool.