She is somewhat openly known to be the bastard daughter of the king from the time he was fostered as young man by Lord Jon Arryn, although she was not acknowledged by her father. She has vague memories of her father, as a big strong man tossing her in the air and catching her. She is nineteen years old, King Robert's eldest child.
At some point after the birth of Joffrey Baratheon, Robert expressed interest in taking one of his base-born daughters (apparently Mya) to court. Cersei Lannister did not protest, but spitefully stated that "the city is not a healthy place for a growing girl", inferring that Cersei would harm her. Robert grew enraged enough to strike her, but did not press the point.