Cosette, the fake daughter, has the ability to cast illusions, and likely affect people's brains directly. That's how she was able to fake having the saintess' abilities, and how she was able to manipulate the father who apparently loved his real daughter more than anyone knew.
The fact that we've been shown, over and over again, that Kiera has trouble emoting and relating to others, seeming stern and harsh when something completely different was on her mind, seems like a very obvious hint for why her father is the way he is, and what his intentions originally were. She, herself, unconsciously made the comparison in the 22nd chapter. And, when you get right down to it, killing off a guiltless child who you raised since infancy just doesn't make sense unless you're an abominable human, which isn't how they're portraying him.
So, yeah. 95% certain, Cosette's ability is related to mind manipulation. It was hinted in the opening prologue chapters, too, when the father was shown to be confused when seeing Cosette's face.