You might be able to check your browser history for clues if you maybe replied, and forgot. Though I don't know enough about how twitter works to know if that would reveal anything. I suspect some stuff is SPA-like and other stuff is traditional web. Do you have a proxy, or anything else that could be logging?

But first you claimed you didn’t wrote the tweet

Occam’s razor: did you get hacked or did you reply and blocked for the taken out of context content