What's the meaning or the best translation of the idiomatic expression "Yes, and I am the queen of England" ?

It means that the other person is talking non-sense.

Like the dialogue in Indiana Jones & The Last Crusade Movie; when Indiana tried to fake a Scottish accent to pretend that he's from Scotland, but it was to obvious for the actual man who came from Scotland and he said to him: "Yes, and I'm Micky Mouse!" 

This is not a familiar idiomatic expression. However, it can be used for unrealistic pop and show.

In Persian language a similar expression is used, " Pidram Sultan Bood". (My father was a King).

I see no idiom here, just a simple statement 

In French, that would be : "Bien sûr, et moi, je suis Napoléon !" ;)