ok.. im confused..

In my understanding, yes he is fl's father

yes, he is the fl's father even tho he doesn't act like it. from my understanding, the fl's father had paris (his son with his lover from the satin family) but the emperor (fl's grandfather through her mother) was responsible/blamed for the satin family's end/death. the fl's father then went on to seduce? the emperor's daughter (fl's mother) and married into the royal family, and fl's mother gave birth to fl. fl's mother took in paris (fl's half brother who has no 'royal blood') and adopted him as a prince even though he wasn't her biological child. the fl's father then went on to trick the fl's mother that he was in love with her until he could finally kill the emperor and the fl's mother to usurp the throne. since he killed with emperor and the only other 'adult' heir (fl's mother), he used this as reasoning to take the throne despite having no royal blood of his own. he did this to empower himself, as well as take revenge, and ensure his son's inheritance. the woman constantly consulting with the fl's father is the fl's aunt, aka the fl's father's sister. the fl's aunt understands that the fl is not to be underestimated, since the fl has the natural and physical characteristics for rulers of their kingdom.
so basically, yes he is the biological father of the fl. he doesn't act fatherly, nor regard her as his daughter, since he despises her and her existence, being the actual blood of the royal family (unlike paris, who is the child of his lover, and has no blood connections to the royal family). however, he knows he can use her in the future by marrying her off for an alliance and not have to see her once this occurs, and he believes she is only a young, stupid girl with no backing, so he decided not to kill her.
sorry for the extra long summary, the phrasing at times in this manhwa is quite confusing so i wanted to be thorough! (●'◡'●)ﾉ

ok ty, was masively confuse because the "info" in the story jumps all over the place.