Hello Sparkita, welcome to Using English!
Both are fine:
1. I was talking to a friend of your father's last night. He said you were an obnoxious little boy, when you were five years old.
2. Did you say that Tolstoy was a friend of your father?
The construction in #1 is known as the "double genitive". It's a perfectly natural English idiom, and is probably the more common of the two – at least, in ordinary usage.
Sometimes people avoid it in more formal usage; you would be more likely to find the #2 version in (for example) a serious biography.
(To my mind, the version in #1 gives a greater sense of "a circle of friends, of which X is one". But other posters may well disagree!)
All the best,