I was watching a 1934 Hollywood film today and one of the American characters used the phrase, Of a Tuesday. I don't think I'd ever heard an American use this in real life or in a film before then, even though I watch a lot of 1930s and 1940s Hollywood movies. I have since heard it used occasionally in films from about the 1920s to the 1960s, but I have still never heard it used outside of films.
Perhaps this, like the MidAtlantic accent in the first half of the century, was and is something used by actors, and in this case writers, far more commonly than by regular (non-theatrical) Americans.
Does phrase Of a Tuesday simply mean the same as On a Tuesday? Is it a commonly used phrase? Has the meaning or popularity changed significantly over time? Are there differences in meaning or usage between British and American English?
So, what are the meaning(s) and usage(s), history, and current popularity of both in American and British English?