WHO’S: a contraction linking the words “who is” or “who has.” (Who’s wearing green today?) (Who’s been a good girl?)
WHOSE: the possessive form of who. (Whose book is this?) (Is he the one whose tie matches mine today?)
TIP: if you aren’t sure which one to use, substitute “who is” in the sentence. If it makes sense, use WHO’S. If not, use WHOSE.