I'm not sure about a specific 'Harry is a alpha werewolf' fanfiction, but you can try searching on fanfiction.net. There are usually a lot of works in the Harry Potter fanfiction section, and you might find one that suits your taste. You can filter by tags like 'werewolf' and 'Harry Potter' to narrow down the search.
In general, werewolf stories are fiction. They've been a staple in various cultures' folktales for centuries. These stories often serve as a form of entertainment, a way to explore human nature in an extreme, supernatural context. For example, the idea of a human transforming into a wolf - like creature during a full moon is a very imaginative concept that has been used in countless novels, movies, and TV shows, but it has no basis in real - world facts.
One popular one is 'The Alpha's Mate' which can often be found on free reading platforms. It tells the story of a young woman who discovers she is the mate of a powerful werewolf alpha. The relationship development between the two main characters is quite interesting.
One of the best is 'Twilight' which features a love story involving a vampire and a werewolf. The werewolf Jacob has a deep, complex relationship with the female lead. Another great one is 'Shiver' where a girl falls in love with a werewolf. The story beautifully portrays their relationship as they face various challenges. And 'An Enchantment of Ravens' also has elements of a werewolf - like character in a romantic fantasy setting.
Werewolf stories have their roots in ancient folklore and mythology. Different cultures around the world have their own versions and explanations of werewolves.