With the way you tell it, they weren't after you personally, but were after a parking violator who happens to have been you. I doubt that you will get much leverage from this, if any.
Assuming that you knew that students weren't allowed to park there, you parked in a place you knew you shouldn't park...You might want to just pay the ticket and not park there again.
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In the absence of information regarding the actual driver, parking tickets are issued against the registered owner of the vehicle. If the owner wishes to present a a defense that someone else was using the vehicle at the time the ticket was issued, they can request a hearing and come forward with their proof. If you were observed by officers as a student who parked in a spot reserved for visitors, you may have been targeted. That is good police work, not the basis for a valid defense. Pay the ticket and next time, don't park in the visitor's spot.
Of course they were targeting you, you had apparently parked in a spot not designated for you. Why would the officer target a car parked correctly? It doesn't matter one iota why they came back to your car, if you were parked illegally you can be ticketed. If you weren't parked illegally, I suspect your post would say something different.