In some fanfiction, a plot twist could be that the Order of the Phoenix discovers that the Time - Turner was actually a trap set by Voldemort all along. He knew that someone from the Order would eventually find it and try to use it to their advantage. But when they do, it activates a dark magic spell that starts to slowly destroy the Order from within. So the members of the Order not only have to deal with Voldemort's external threats but also this internal danger caused by the Time - Turner.
One interesting plot twist could be that Hermione discovers a hidden prophecy within the Order of Phoenix that directly relates to her and her friends' destinies. This could lead to a whole new set of adventures and challenges as they try to figure out what it means and how to prevent or fulfill it.
You can try fanfiction websites like FanFiction.net or Archive of Our Own. Just search for 'Order of the Phoenix Time - Turner' in their search bars. There are often many talented writers who create interesting stories around these concepts.
Maybe a plot where the Time Turner malfunctions and sends a character into an alternate timeline within the fanfiction's universe. This would lead to them having to figure out how to get back while also dealing with the differences in this new timeline, like different relationships between characters or altered magical laws.
In some 'Game of Thrones' Phoenix fanfiction, a common plot twist is that the phoenix has the ability to resurrect dead characters. This completely changes the course of the story as characters who were thought to be gone forever return. For example, in one fic, Ned Stark is brought back by the phoenix's magic, which then sets off a whole new chain of events as he tries to reclaim his honor and seek revenge on those who wronged him.
One idea could be that Hermione, using the Time - Turner, accidentally goes back to a time when Lucius was a young Death Eater in training. She tries to subtly change his path, which leads to a series of events where they form an unlikely alliance. They might start to understand each other's motives and values more deeply.
One idea could be Snape using the Time - Turner to go back and change a crucial moment in his relationship with Lily. Maybe he tries to prevent her from getting involved with James Potter. Another plot could involve Snape using it to gain an edge in his spying for Dumbledore during the First Wizarding War. He could go back in time to gather more information about Voldemort's early plans.
One idea could be that Hermione accidentally travels too far back in time with the Time - Turner and ends up in Severus' student days. She has to navigate Hogwarts without being detected while also trying to figure out how to get back. And Severus stumbles upon her and at first is suspicious but then realizes she's from the future and they start to work together to fix the time - line.
In some fanfictions, a plot idea is to have Harry gain a new power. In the context of 'Harry Potter Order of the Phoenix', it could be a power related to his connection with the late Sirius Black. For instance, he might be able to communicate with Sirius in a new way, like through dreams more vividly. This could change the way he approaches his fight against Voldemort and the Death Eaters. Also, a plot could involve the Ministry of Magic having a more complex internal struggle that affects the Order's operations.
One idea could be Percy getting involved with the Order of the Phoenix somehow. Maybe he's sent on a mission by the gods to help them out. He could use his water powers in new and creative ways within the wizarding world, like using water to put out magical fires or even to disrupt dark magic spells that rely on dryness.
Well, sometimes the fanfictions might have a plot twist where the Deathly Hallows themselves have different powers than what was originally thought. Maybe the Elder Wand has the power to not only be unbeatable in duels but also to reverse the effects of dark magic, which completely changes the dynamic of the story. This could lead to a situation where characters who were previously doomed by dark magic curses are suddenly cured, and it alters the relationships between the different factions in the wizarding world.