When a user is suspended, they receive a message (a "mod message") in their Stack Exchange inbox giving the reason for the suspension. They can then write a response to that message. If they believe that the suspension is in error ("Did you mean to suspend the user ff523, not ff524?") this is a quick way to clear up the misunderstanding. Note that you can't keep sending multiple responses, one after the other; you get one response per mod message, so use it wisely.
All mod messages and the responses to them are copied to all the diamond moderators on the site. So if there's a rogue mod acting up ("You voted to close my post? See how you like a ten year suspension!"), other mods will see and intervene.
Finally, if the moderator team on Academia.SE is not willing to lift your suspension that you believe is unwarranted, you can use the "contact us" link in the footer of every SE site to ask the SE team to look into the matter.