My mother was from Philadelphia, Pennsylvania. And she used "me" when speaking instead of saying "my". For example: "that's me house". She was second generation British in the USA. So whenever I hear people on TV say it, I am reminded of her. However, I never used "me" the same way she did. I suppose my speech was ...
Although the answer by @Colin Fine is correct, it doesn't completely cover the usage.
John: Bill, your grammar isn't good, I think you should study more.
Bill: Huh! Since when are you an expert on grammar? I get better marks than you do.
It's a common informal way of saying "I don't believe that is correct".
On the surface it is saying "As far as I know, X is correct. How long has what you said been right?"
It is slightly combative, but less than saying directly "That's wrong".
a) “Who was Sarah with?”
b) “Who was with Sarah?”
These are both correct but they have a different emphasis. In (a) Sarah was with someone. We get the impression that the someone was more important/famous/significant than Sarah. In (b) we get the impression that Sarah was the main character and someone was tagging along with her.
The above distinction is ...