sickness insurance in germany,,

There can only be extreme reasons why a public health insurer like the AOK can reject someone - like for nonpayment or fraud. But it is for legal residents, not traveling tourists.

The rules, unlike what Tom wrote above, are extremely complicates and there are many pitfalls, especially for foreigners new to Germany.
In any case, these rules are supposed to determinate if and which health insurance you must or cannot join (you rarely have a choice here!). Problem is that those rules are not fully understood by anyone, including the insurance officers.
If you want to know for sure, engage an independent health insurance adviser (for a fee - the free ones are useless).

For clarification to Beppi’s response, yes there can be complicated rules with health insurance as to which group one needs to join or if one is allowed to opt for a private rather than public one. But the general rule is simple; every German resident has to be insured and everyone can take a public option.

It won't answer every question but the Wkipedia entry gies a good run down on the system:

https://en.wikipedia.org/wiki/Healthcare_in_Germany

Sorry, not everyone can join the public health insurance in Germany.
It depends both on your visa and status in Germany, as well as how you were previously insured.
I know from first (my own and my wife) and second (foreigners I help in these matters) hand that rules are too complicated for even the insurance officers to understand - we got completely conflicting information from various insurers and in the end chose those that gave the answer we liked most.

lol yes the complicated German way..rules and rules,,i must first wait for their response to my application.after 3 weeks still no reply,,the most best excuse is we have a big backlog due to all the assailants applications,,

yes its so complicated,,,,,but if i cant get public and cant afford private what thenn

anthony hofmeyr wrote:

yes its so complicated,,,,,but if i cant get public and cant afford private what thenn

Then you can and should not move to Germany (thus are the rules - not my personal opinion!).

lol.was expecting that reply,,then why did thy give me my visa,,and when i was at Aok in 2015 thy said no problem i can get covered

the problem is i am here in Germany already,,not a question then i shouldnt come,,if of the other groups can get  can get covered by state health why cant i get,,i at least have a monthly pension i am getting,,im not getting any state money..i get my own money,,

The visa-giving authority does not need to care whether you can afford the necessities of life in Germany.
Unless you are employee (for which the employer pays half the health insurance premium)  or in some other privileged group (e.g. German pensioners - your presumably foreign pension does not apply), the minimum public health insurance contribution is around €370/month. If you find this steep: Private insurers charge more!
55 years of age (which, as a pensioner, you might exceed) it a maximum age to join the public scheme (but of course there are also exemptions from this rule).