thank you for addressing your situation with us in the community .
If you have been caught without ticket once and payed your fine/ paying your fine it not a big deal but if you have been caught 3 times then it is a criminal act and you could face court charges. Make sure you pay your Inkasso fine as well as they can come up with a Vollstreckungsbescheid( this involves the court as well).
The Schufa( if there are minor things) does not stop them to issue your residence permit papers but if the acts become a court decision then they will have it in your file as negative point that might influence their decision. However it is not the case if you have been caught once and have a negative Schufa because of that.
I hope this can help you, if you need more specific informations please do not hesitate to address your questions here in the community.