The daughter Christopher Pike knew only in the full and happy life he experienced with Marie Batel through her illusion.
Juliet is the daughter of Christopher Pike and Marie Batel in the illusory lifetime Batel created for Pike in New Life and New Civilizations, before she became the Beholder guarding the Vezda.
In Like Chronitons Through the Hourglass, while Trelane traps the crew in a soap opera, Pike meets Juliet. She tells him that something that did not happen can still be real, and the two reconcile before she fades away. The meeting helps Pike begin to face his grief.