I would like to see evidence related to speeding ticket

While I am not familiar with Ohio law, I doubt that, now that the action is over, you have any basis for a "defendant's motion."  You are no longer a defendant - you pleaded guilty and paid the penalty.  Although theoretically you could make a motion to vacate the judgment, you have articulated no basis why the judgment would be vacated, since there was no reason why you couldn't have fought the ticket before, instead of pleading guilty.  You might be able to get the information you seek through a freedom of information request, but I don't see how it will help you.