I think this is Nessa the heroine of Fractale’s anime. Nessa is a “doppel” copy of Phryne’s younger self, composed of “data” important to the Fractale system. Her existence is unique because, unlike other doppels, she can be touched, but only by people she chooses.
Her character is very cheerful, energetic, and carefree. Clain meets Nessa for the first time when she suddenly appears out of Phryne’s brooch. She smiles a lot and likes to explore, even occasionally dragging Clain into trouble. Her motto is often quoted to be that she “loves love.” Like Clain, she expresses that she simply wants to be together with her friends.
The anime aired in Japan between January and April 2011 on Fuji TV’s Noitamina programming block. A manga illustrated by Mutsumi Akasaki was serialized in Square Enix’s Gangan Online between September 2010 and November 2011.