Don't @ me is a phrase on Twitter when you say something and you don't want people to respond directly to you. They can retweet, like, etc. but don't respond directly because you don't care what people have to say about your opinion.

Anatidaephobia is defined as a pervasive, irrational fear that one is being watched by a duck. The anatidaephobic individual fears that no matter where they are or what they are doing, a duck watches.

Anatidaephobia is derived from the Greek word "anatidae", meaning ducks, geese or swans and "phobos" meaning fear.

When someone says "Dont @ me" they're saying "dont reply to me" or "dont try and argue with me" ect. Most of the time its used as a joke.