Maybe Dobby could be an unexpected ally. He could use his magic to create distractions for the other contestants or help Harry find a hidden passage in the maze. Another possibility is that one of the Hogwarts ghosts, like Nearly Headless Nick, decides to assist Harry. He could float through walls and spy on the other champions' movements and relay the information to Harry.
In some fanfictions, Harry might struggle with PTSD after the third task. The trauma of facing Voldemort again could haunt him, causing nightmares and making him more withdrawn. He might also become more determined to defeat Voldemort, spending all his spare time studying dark magic defenses.
One plot twist could be that the maze reveals different illusions for each contestant based on their deepest fears. For example, Harry could see Voldemort killing his friends instead of the normal obstacles. Another could be that the cup at the end is a fake and leads to a more dangerous trial. Or perhaps one of the other champions teams up with a dark wizard within the maze to try and eliminate Harry.
In many fanfictions, Harry's view of Dumbledore could shift. After the third task, he might start to question Dumbledore's actions and motives more. He might wonder why Dumbledore didn't protect him better or why he seems to be keeping so many secrets. This could lead to some tension between them. At the same time, Harry's relationships with the other houses could improve. Gryffindor already admires him, but now Ravenclaw might seek his knowledge about the Dark Arts, and Hufflepuff could respect his courage. This could make him more of a unifying figure at Hogwarts, despite the Slytherin opposition.
Harry Potter himself is often a central character in these fanfictions. Since he was the one who originally faced the dragon task in the Triwizard Tournament, many fanfic authors like to explore different scenarios with him in the same situation.
One possibility could be that Harry, as a Dragon Animagus, uses his new form to his advantage in the First Task. He might be able to outmaneuver the real dragon more easily, flying around it and confusing it. This would give him an edge in retrieving the golden egg.
One interesting plot could be a character having to train a dragon for the task in a completely new way, using magic that was previously undiscovered. This would add an element of mystery and innovation to the story.
Well, in a fanfiction of the Harry Potter first task, Harry could find out that the dragons have been enchanted by a dark wizard who wants him to fail. So, he has to not only deal with the dragons but also break the enchantment. Or perhaps Harry has a premonition about the task in his dreams, and with the help of Dumbledore, he learns how to use this new - found ability to his advantage during the task. Also, a fun idea could be that Neville gives Harry a magical plant that can temporarily paralyze the dragon, but Harry has to figure out how to use it correctly in the heat of the moment.
A young dragon tamer from a far - off land could be an interesting addition. This character could have a deep understanding of dragons and offer Harry some advice on how to approach the task. Maybe they have a special bond with one of the dragons in the task and can communicate with it, which could add an unexpected twist to the story.
If Harry were a Dragon Animagus in the First Task, it would change the whole dynamic. He could use his dragon form to create a diversion. For example, he could make the real dragon chase him away from the egg, and then quickly transform back and snatch the egg. Also, his dragon form might have some special abilities like breathing fire in a controlled way to fend off the real dragon if it attacks.