He might be extremely confused at first. Since he doesn't have a sister in the original story, seeing her in fanfiction would be quite a shock. He could also be intrigued, wondering how the author has developed this new character and what kind of relationship she has with him in this fictional scenario.
Harry Potter might initially dismiss it as just some strange idea from a fan's imagination. However, as he reads on, he could start to get drawn into the story. He may find himself imagining what it would be like to actually have a sister. He could start to feel a connection to this fictional sister, perhaps even feeling emotions like love and pride as the story unfolds. And depending on how the fanfiction portrays the sister, he might even start to consider how having a sister could have changed his life and his experiences at Hogwarts. For example, if the sister is also a powerful wizard or witch, he might think about how they could have faced Voldemort together.