being born prematurely, later or anything doesn't affect your sign. you're talking about a due date vs something literal. your "sign", which is basically just what sign of the zodiac the Sun is in when you are born, is based on where it was the moment you were born. even "cusp" babies don't fall back and forth between being 2 different personalities just because they were born the day of a sign change. the Sun is in one sign or another. like Lucky said, there are plenty of other planets and whichever sign those planets are in will add other sign signatures to your personality. the part of your personality (planet) in question is what the sign is affecting. so, for instance, the Moon shows your emotional disposition, your habits, your home, Mother, important females in your life.. let's just look at the emotional aspect of it. someone who's Moon is in Aries will be very emotionally impulsive, emotionally fiery vs Moon in Capricorn which would be someone who is more emotionally serious, emotionally withdrawn. but this is just your emotional nature. so, people may see this Capricorn side of you even though you are a Sagittarius, Taurus, Aries, Gemini, etc.
anyways, sorry to jump in with all of this Astrology. just wanted to explain some confusion around that topic that was just briefly brought up.