Such silly stuff have no relevance for your permit.
For the future, if one is so unlucky, had not seen a Verboten sign, and got a letter from a private individual do pay a silly sum (above CHF 50). DO NOT DO ANYTHING. Wait and relax. Important do not contact the one who sent you the letter, as you may admit your fault.
Unlike regular parking tickets, where the holder of the car is ultimately liable for the ticket, such a parking infringement can only be enforced against the one who actually did it. Many options, as family members have no obligations to snitch on each other.
Once again: If it goes to court the money goes into the community chest. Outside court into some privates individual pocket.