“There is actually no such thing as cusps,” the twins say. Due to the way the Sun transitions from signs, it’s not possible to be under two at the same time. There is an exact moment when the switch happens.
Of course, that’s not to say you can’t have a combination of traits from different signs. After all, that’s what your birth chart is all about. A Scorpio-Sagittarius cusp, for example, might actually be a true Scorpio, but perhaps their Venus is in Sagittarius. As far as the sign the Sun was under while transitioning from one to the next, though, it’s never under both.
“In order to know your Sun sign (and you only have one!),” the twins note, “you need your exact minute of birth, along with your time and date.” (You can map your birth chart with the twins’ handy natal chart generator if you haven’t already).
Sorry to burst your bubble if you were sure of your cusp identity, but again, it doesn’t mean you don’t have that sign’s energy somewhere else in your chart. But when it comes to your Sun sign, there can be only one.