FOUND, don't see any way to remove this.
Like many other dramas, it begins with the head of a noble family being falsely accused and his entire family condemned. When soldiers go to kill his young daughter, the nanny's granddaughter is there as well. The nanny identifies her granddaughter as the noble child. She raises the noble girl and has plans for her, which include studying for an exam (likely male only, so I believe there will be cross-dressing).
Later: It's Song of Youth. Some details wrong. Family is banished, not condemned to death. Also, it's the nanny's daughter taken away by soldiers.
