There's no such thing as an extra sign. People who say there is are confusing signs with constellations. They're not the same thing.
An astrological sign is a 30 degree section of the sky, measured from the ecliptic (the sun's path around the earth, or rather, what looks to us like the sun's path around the earth. The ecliptic actually reflects earth's orbit around the sun). Each of those sections is associated with a constellation that, at the time the signs were named, actually was in that section of sky for the most part.
Thanks to the wobble of the earth's axis, the constellations no longer align perfectly with their namesake signs. But the astrological signs are still the same. They don't change just because a constellation moves. Neither does the existence of another constellation create another sign. Since a sign is, by definition, 30 degrees, and the ecliptic is, like all circles, an exact 360 degrees, there can never be any more or any less than twelve signs. It's impossible to divide 360 by 30 and get anything else.
What I'm describing here is tropical astrology, which is what Western astrology is. Vedic astrology is a bit different, and does match the signs more closely with the constellations (that's called sidereal astrology), but even there, only the original zodiac is considered. Vedic astrology also has 30 degree signs, which, again, makes it mathematically impossible for there to be any number other than twelve.
So if you were born in the last week and a half of March or first three weeks of April, your sun sign is Aries. Nothing changes that. You may have a Pisces sun in Vedic astrology, because everything in a Vedic chart is 23-24 degrees earlier than in a Western one, but that has nothing to do with additional constellations, and sun sign is not considered the determinator of personality in Vedic astrology.
However, cookbook descriptions of sun sign traits rarely fit actual people with those signs. Your personality is shaped by your whole chart. Your Aries sun is modified by its house placement and the aspects it makes, and what you think of as your personality, and what others see as your personality, is typically a much closer match to your rising sign than your sun sign. Where Aries comes in for you is that there's some sort of Aries message in your core personal growth. Maybe you thrive on personal challenges. Maybe you are, in some sense, a pioneer, someone who tries new things first. Maybe you have a social activist bent--that's a very common theme for Aries. You might manifest Aries in a quiet way instead of a loud, noticeable way, but it's there one way or another.