An apostrophe is the punctuation mark used to show possession in English, as in phrases like the anthropologist's singing or women's independence. It is also used to mark the omission of letters in contractions such as don't or it's, but the question specifically asks about the possession function.
A hyphen joins words or word parts together, such as in well-known, and does not indicate ownership. A semicolon connects two closely related independent clauses and has nothing to do with possession. A period simply marks the end of a sentence and carries no possessive meaning at all.
Since only the apostrophe is used to show that something belongs to someone or something, the correct answer is option 2.