Assuming that you have a six months probation period as normal in Germany, you cannot really do anything. They are allowed to terminate your contract for basically no reason. So if they decide to fire you, and say nothing about why, then you have zero options.
If they quote their three strikes system or reference your illness in any way, you will need a local lawyer to find out whether you have chances to sue. However, this being Germany, you will not get swift justice and if you get justice, the amount they owe you will be the amount you would have earned had you worked there, minus the money you actually made. So as an example, you get fired, you find a new job for the same pay after two months, so a year from now, when the queue of the court has sufficiently advanced to discuss your case, if found in favor, you will get two months pay. The two months that you lost out on while looking for a job. As soon as you had a new job with the same pay, you have incurred no damages and you get no payments from them.
Please note that, fair or not, obviously your next employer will be very reluctant to hire a candidate that sued their former employer after being let go in the probation period. And the judgement being about a year out, they have no idea what happened or who is right.
So your best bet is to be on your absolute best behaviour at least until your probation period is over. That might include lying to people, apologizing for things you think are correct, but they think are your mistake. Whether your integrity is worth your job is up to you.
The other route to go would be to go out for a job search immediately. If they are set on firing you, they will. The question just is, whether you could get some money out of them for doing so illegally. Find a company you like to work for, that treats their employees with more respect and that you can treat with more respect. As it's your only real option, you might as well start today. Take control over your life, don't wait to be the passive victim of something. That never feels good, whether it is legal or not.
If you sent out letters now, you also control the narrative. "I need a new job, the old one kicked me out during my probation period" has a very different story than "I saw it wasn't a good match and decided to look for another job. It seems my employer thought the same thing, they have since let me go."