The correct female possessive pronoun in such sentence constructions is “hers,” which means “that which belongs to her,” so the grammatically correct sentence is “I am a fan of hers.” “Her” is used without a following noun and is equivalent in meaning to the adjective “her.” The form “her’s” is not a valid possessive pronoun form in English. Forming the possessive by affixing apostrophe-s is done only on nouns, as in “Alfred’s,” “man’s fate,” and “the cat’s paw.”
