I just got an AUP notification stating that I downloaded a movie that I have no idea of what it is even about. How do I deal with this and prevent it from happening again. Nobody else has access to my modem or internet.

Send an email to cox.help@cox.com with your full name, complete address and your situation.

If Cox claims a download has violated their policy, somebody at Cox will have the metadata to verify the download.  Cox should then provide you the data to help figure what had happened.