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.

They should have the time, item, and IP address of the AUP in question. Do you have Hotspot enabled? I always wondered who it tracked to when someone goes on someone else hotspot. The IP of the hotspot or the username signed in with? It doesn't seem to track bandwidth to the username, so I assume the IP.

Believe it or not, there are MANY ways this can happen. There are multitudes of software out there, things like Popcorn time, Showbox, Stremio, Kodi, Crackle, Cinema APK (HD Movies),Terrarium TV, Titanium TV., CatMouse APK., UnlockMyTV,  TeaTV, CyberFlix TV, TVZion and more. These all and others use bit torrent to allow you to watch tv shows and movies on cell phones, tablets, computers, tv's, fire tv, and other methods. 

When you say no one else has access, no spouse, partner, kids, friends? I know someone who had a friend come over, gave him the wifi pwd, and next day they were suspended, seems their friends phone was downloading a movie.