What if i catched some mot****er, who is using one of my wallets - how can i prove that it's mine?

Signing a message is something on their wallets is something that people have been doing since bitcoin's public release. This is also the reason why we found out whose wallets are of Satoshi Nakamoto's ownership, because he signs a message on his wallets. In any case, there are also a few other techniques that other users employ like keeping timestamps of their wallet's age and other stuff. But all of these are really dependent on what wallet type you use.