Well, it depends on the specific fanfiction. There are countless fanfictions out there, and while some might make Harry the heir of Salazar Slytherin, others may not follow this concept at all. Some fanfic authors like to subvert the expectations set by the original books and come up with unique ideas like this to explore different aspects of the wizarding world.
One consequence could be a change in how the other characters view Harry. The Gryffindors might be more suspicious of him, while the Slytherins could either try to use him or see him as a threat to their own status. For example, Draco Malfoy's relationship with Harry would likely be even more complex.
😋I recommend you the novel, Harry Potter: Salazar a Thousand Years Later! It was a light novel, a derivative doujinshi novel, about Salazar. The story of Slytherin leaving Hogwarts and using time magic to travel a thousand years into the future. In 1981, Salazar had to face a sickly vampire who might want to eat him at any time and a Horcrux hat that carried the soul of his good friend and encouraged him every day. In addition, there is also the daily life of the single female lead. I hope you will like this novel.
In a lot of these fan fictions, Harry is often the hero, but Malfoy can be a very interesting anti - hero. His family's dark past and his own growth throughout the series make him a character with a lot of potential for development in fan - created stories. And Salazar Slytherin, as the founder of one of the Hogwarts houses, brings an air of mystery. Fans are always interested in exploring his character, whether he's portrayed as a villain or someone with a more nuanced backstory.
One possible plotline could be that Salazar Slytherin's long - lost magic has an unexpected connection to Harry Potter and Draco Malfoy. Maybe it reveals a hidden prophecy that involves the two boys working together to save Hogwarts from a new dark threat.
I read a fanfiction once where Harry being the heir of Slytherin led to a whole new dynamic in the wizarding world. The story explored how the other houses reacted, especially Gryffindor. It was fascinating to see Harry struggle with the duality of being seen as both a hero from Gryffindor and the heir of the supposedly 'dark' Slytherin.
One common theme is identity crisis. Harry has always identified as a Gryffindor, so finding out he's Slytherin's heir makes him question who he really is. Another theme is prejudice. People in the wizarding world often have negative views of Slytherin, so Harry has to deal with that when his heritage is revealed.
I'm not sure which book you're referring to. I can help you find some relevant information about the novel, but you need to provide more context and information so that I can help you better.