Dear @Cj,
Welcome to the Wefugees Community and thank you for your question!
First of all, if you are sick, you should see a doctor and you most probably will get a medical report. In Germany, you don't have to quit your job because of an illness and the employer will pay your salary for up to six weeks you are staying at home for the same medical issue. After the six weeks, your health insurance might grant you a monthly allowance which is called "Krankengeld" (the amount is dependent on your regular salary).
The Bundesagentur für Arbeit is paying the unemployment benefits or "Arbeitslosengeld 1". In order to receive it, you have to fulfill certain conditions. Having worked for at least 12 months during the previous 30 months while contributed to the mandatory insurance (not a typical Minijob in that sense), for instance. Please be aware, that you may be excluded for up to three months ("Sperrzeit") in case you got unemployed voluntarily (quit yourself without a serious reason).
The Jobcenter is granting the so-called "Arbeitslosengeld 2" which functions like a social net and might be granted in case you can not cover your life expenses with your income or other allowances (as the Arbeitslosengeld 1).
However, please note that you need to get a permission of the respective agencies in case you want to travel or go on vacations while you are receiving Arbeitslosengeld 1 as well as Arbeitslosengeld 2. As far as I know, up to 3 weeks per year may be granted. If your doctor recommends and prescribes a rehabilitation programme (Reha), different rules may apply.
I hope this helps to get an overview and please don't hesitate to get back to us with any further questions.
All the best,
Meike