one says 'a friend of mine' which means "a friend of tom's" will be correct (converting the possessive pronoun to possessive noun). then why is "a citizen of Japan's" wrong? when does one use apostrophe with of and when not?
You're correct in your suspicions. Saying "a friend of mine" does seem to double up on the possessiveness, and strictly speaking, doesn't make good sense. But it's just the way we say it, which always trumps intelligent analysis ...