<spoiler>There was no cheating. Basically current Emperor's bro named Lucas Wilhelm(?) woke up in Gaspar's body after someone cursed his soul to possess another body. Based on Leonora's estimates his soul has been there for at least 4 years (around the the time she was conceived). When he initially woke up in Gaspar's body, he saw a naked woman - Noel (Leonora's mom) immediately sensed something was off and attacked him asking him who he was. Leonora did the same thing when he came home and effectively rejected her flower bracelet gift, saying he wasn't her dad.
The reason why Leonora is known as an illegitimate child was because she inherited Lucas's mana while his soul possess Gaspar's body. He hasn't been able to unravel the curse that got his soul stuck there and he occasionally takes over Gaspar's body. All anyone knows about Lucas is that he's disappeared and emperor took over.
From my understanding, Gaspar has moments of clarity when he's back to himself and his usual loving father figure - though it's not clear if he's fully aware Lucas possessed his body. When Lucas tries to suck Leonora's mana to replenish his own, Gaspar wakes back up in his body and tells her to run. He then tries to take a sword and stab himself to protect her but Lucas is fighting with him to stop his hand from moving. MC then bites his arm to prevent him from attacking himself and Lucas took over again. Gaspar is later conscious in his body again and seems like it flips back and forth.</spoiler> from novelupdate
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Spoiler anyone?