Are you constantly getting messages from your followers on Twitter saying that you're sending them these fake messages, that're usually like "you ar famous now haha *facebook link*" or "Someone's talking about you *facebook link*"? Well a lot of people think these are caused by a virus on your computer. Well to be honest, I highly doubt they're spawned from viruses.
To stop any spam direct messages being sent from your account to your followers on Twitter, please check your "Apps" section in your "Settings" area, as it would 99.9% of the time be YOUR fault as YOU have allowed an application permission to use your account - without checking properly what permissions you're allowing it to use, which a majority of the times it'll say "Can access and send Direct Messages" - which you can see in the picture below (1) and some applications will just ask to read and write (i.e; post tweets) (2).
So to stop any, then please check your "Apps" and click "Revoke access" on any that have the permission to access and send "direct messages" (that ain't official Twitter apps). This will stop any false DM's being sent and stop you losing followers.