LF: specific manhwa, fake daughter

I've ready too many reincarnation/transmigation manhwas to find it
About a girl that made a plan to escape once the real daughter has been found since she's not related by blood with the king. I remember the king finding her but she says she does not want ro go back (I found this dumb so I stopped reading jt but I want to see what's the progress between the fathed-daughter relationship)