One great 'Percy Jackson Twin Fanfiction' is 'The Twin Heroes of Olympus'. It follows the adventures of Percy's twin siblings in the world of Greek mythology. The story has exciting battles and interesting character development.
Fanfiction.net is another good place. There are a lot of Percy Jackson - related fanfics there. Look for the specific category or use the search function to narrow down to the twin fanfictions. However, the quality may vary, so you might need to sift through some to find the really good ones.
Percy would likely be more in tune with the concept of home and family. Since Hestia represents the hearth, Percy might be more nurturing and protective. He could develop a stronger sense of responsibility for the well - being of his friends as if they were his family.
One possibility could be that she shows up at Camp Half - Blood unexpectedly. Maybe she was raised by a mortal family all this time, not knowing about her demigod heritage. When she arrives, she has powers similar to Percy's but also some unique ones, like the ability to communicate with sea creatures in a different way than Percy. This could lead to all sorts of adventures and conflicts within the camp as everyone tries to figure out who she really is and what her role will be.
One idea could be that Percy's twin connection to Hestia gives him the power to control and purify fire in a unique way. For example, he can use it to heal as well as to fight monsters. Another plot could involve the twin bond causing Percy to have a stronger sense of home and family, leading him to create a safe haven for demigods using Hestia's influence.
You can start by giving her a distinct personality. If Percy is brave and impulsive, make her more cautious and calculating. For example, she could be the one who always thinks twice before jumping into a fight, analyzing the situation and coming up with a plan. This contrast in personalities can create interesting dynamics within the story.
One possible plot twist could be that Percy has hidden powers related to Kronos. Since Kronos is a powerful Titan, Percy might have some latent abilities that are similar but not as malevolent. For example, he could have a unique control over time on a small scale, like being able to slow down time briefly in a battle to gain an advantage. Another plot twist could be that the gods initially mistake Percy for being as evil as Kronos due to their relation. This would lead to Percy having to prove his loyalty to the gods and his friends all over again. He would face a lot of distrust and have to overcome many challenges to show that he is not like his 'twin' in nature.
He could start off as a rival to Percy. Maybe they both have their eyes on the same girl or they are competing for leadership in a demigod mission. But then as they get to know each other better, they become friends and respect each other's abilities.
Well, in a fanfiction like this, perhaps Percy's twin brother was separated from him at birth due to some prophecy or dark magic. The twin could have been raised by an enemy of the gods. As he grows up, he starts to question his loyalty to those who raised him when he begins to discover his true heritage. Eventually, he and Percy meet and have to reconcile their differences while also dealing with the threat that the twin's 'adoptive' side poses to the world of the gods.
Another plot could involve the twin sister being cursed. This curse could be related to her connection with the sea as well. For example, every time she uses her powers related to the sea, she experiences a great deal of pain. Percy then has to find a way to break the curse. In the process, they discover an ancient prophecy that not only involves Percy but also depends on his sister's role in fulfilling it.