Yeah so I stumbled across this today whilst writing a scene. One of my characters quotes someone, I mean would just be: "Ey, Tony! So Big Billy ses to me, 'Even if I did know, I wouldn't tell you ya prick!' You believe that shit?! Took me four me toes before he snitched—stubborn fat bastard!" Ignore the actual dialogue, I just made that up lol. Just slap a few apostrophes around what the character is quoting? Or is there some special rule I'm seemingly missing?
Using a single quotation mark is correct. That's the way it's done when you have quoted material inside other quoted material. Some countries (like England) enclose dialogue in single quotation marks, so whenever you have quoted material inside that, you would use double quotation marks. For example: 'Tony! So Billy said, "Blah, blah." You believe that?'
@thirdwind is correct. And just to be clear, American English follows the method you used and that third wind mentioned in the beginning of the post, with single quotes surrounding the line(s) the character's quoting from someone else, all composed inside the double quotes.
