Using a footer without a cite

That’s probably how I would structure the HTML, although without more context, I can’t say for certain.

You should not use a <br> tag here. If you want more space, use margins or padding. I’m sure we’ve explained this more than once.

If the quote is from a written work, then reference to the source would usually be included somewhere, I think.

Again, without seeing the rest of the page I’m only guessing, but you should be able to simplify the CSS. Instead of blockquote p.quote and blockquote p.author, the classname alone will probably suffice: .quote and .author. Keep it as simple as possible.

Note: You have wandered well away from the topic of this thread. If you want to continue discussing methods of styling blockquotes, then please do so in your other thread.