He might be initially shocked. I mean, he's used to all the demigod stuff, and then finding out his mom has wizard powers would be a whole new level of surprise.
Percy might be initially very confused and hurt. He may try to find his sister and understand why she has left him. He could also become very angry and feel betrayed, which might lead him to take some rash actions.
Female Percy could also be determined. Instead of wallowing in self - pity, she decides to use the banishment as an opportunity for self - discovery. She could set out on a journey to find out more about her powers or her past, believing that there is a greater purpose behind her banishment.
Eventually, he may reach a point of self - reflection. After some time, Percy might realize that his family's feelings are also important. He could start to reevaluate his actions and his priorities. In some fanfictions, this could lead to him trying to mend the relationship with his family, even if it's a slow and difficult process.
He might be angry at first. After all, he has done so much for Olympus. He could feel betrayed by the very beings he has fought to protect.
He might be really angry at first. He's given so much to the camp, and being kicked out like that without a proper explanation would make him furious. He could storm off, vowing to find out the truth and clear his name.
Percy could also react with a sense of determination. Instead of being defeated by the injury, he sees it as a challenge. He starts to figure out what made Artemis hurt him in the first place. If it was a misunderstanding, he tries to clear it up. If it was something more malicious, he starts to plot his revenge. He uses his own wits and the powers he has to either heal himself or find a way to make Artemis see the error of her ways. He might also seek the help of his friends, like Annabeth or Grover, to come up with a plan to deal with the situation.
At the start, Naruto might be in shock. He can't believe that his own family would do such a thing. After the initial shock wears off, he would probably be determined to show them that they made a mistake. He would go on adventures, learn new skills, and meet new people. Through these experiences, he would become more independent and self - reliant. And when the time is right, he might try to confront his family, not in a vengeful way, but to show them that he has changed and that their banishment was unjust.
Naruto might initially be heartbroken. He has always longed for his father's love and acceptance, so being disowned would be a huge blow. He could go into a state of depression for a while, withdrawing from his friends and normal activities. But then, Naruto is a fighter. He would likely start to question his father's decision and try to find out the real reason behind it, vowing to prove himself worthy if there was some misunderstanding.
As time goes on, Naruto could become angry. He might feel betrayed by his family's lack of attention. This anger could fuel his determination to become stronger on his own, without relying on his family. He may start to train harder and focus on achieving his own goals, using the rejection as motivation.
Naruto may also try to find solutions. Despite the heartbreak, his optimistic nature might still shine through a bit. He could start to search for ways to mend the relationship with his parents, whether it's through magic in the Naruto world or by trying to prove his worth to them.