Yeah, he is, but never told anyone because if he gets discovered he will get hus title removed and be getting his arms and eyes cut... but she discovered after finding a memory magic stone?
i think the translation of the chapter that shows
the memory where he is holding her its twisted, instead of "your child" should be "our child" when he speaks, but thats just my speculation
Oh yeah, it was confirmed really early on in the story. Basically she had found a memory magic stone that had belonged to her mum in the house she grew up in (before taken to the palace) in one of her past lives, where their parents are talking. She pretty much keeps saying from then on that he is her dad, no doubt about it (which is true). Another evidence is her having both divine and magic power in her!
So is he really her father?? I didn't see an official confession about that, so i'm still confused