In this fanfic, a really cool plot point might be how Moody's artificial eye plays a part in Harry's upbringing. Moody could use it to teach Harry about seeing through disguises and hidden threats. Also, Moody's no - nonsense attitude might make Harry a more disciplined wizard. He might not tolerate any sloppiness in Harry's magic, which would lead to Harry being a more precise and powerful wizard in the long run.
Well, since Moody is a very vigilant and somewhat paranoid character, Harry would be more observant. He would constantly be on the lookout for danger, like Moody does. His sense of humor might also be a bit darker, influenced by Moody's experiences in the wizarding wars. He might not be as quick to make friends, as he would be more focused on who could be a potential threat. Also, his view of authority might be different. Instead of always looking up to Dumbledore, he might question authority more often, as Moody is a bit of a maverick in his own right.
Another good character to pair with Moody might be Sirius Black. Given their both having experience with the dark side of the wizarding world, they could team up in a fanfiction to take on some new threat or solve a long - standing mystery that has to do with the dark wizards.
One interesting Moody fanfiction could be where he mentors Harry in a more in - depth way outside of the classroom. It might explore Moody's past experiences with dark wizards and how he imparts that knowledge to Harry for future battles.
One great Hermione and Alastor Moody fanfiction is 'The Unlikely Alliance'. It explores a scenario where Hermione has to work closely with Moody on a dangerous mission. The story does a great job of building tension and showing their different personalities interact.
Harry would likely be more gruff and less trusting. Growing up with Moody, who was always on guard, Harry would have learned to be more cynical. He might not be as quick to make friends as he was in the original story.
Harry would be more cautious. Moody's paranoia would rub off on him. He'd be constantly on guard, not as quick to trust people like in the original series. For example, when he meets new classmates, he might be sizing them up for potential threats instead of being friendly right away.
In these fanfictions, a really cool plot twist could be that Moody, because of his experience with the dark arts, has knowledge of a secret power within Harry that even Voldemort doesn't know about. He nurtures this power in Harry, which makes Harry a completely different kind of threat to the dark forces. Maybe it's a power related to the ancient magic of the founders of Hogwarts that was passed down in a way no one expected.
Another common theme is adventure. Picture Hermione and Moody going on some secret mission to take down a new dark wizard threat. These stories usually involve a lot of action, like dueling and sneaking around in dangerous places.
Perhaps Moody, being a very experienced Auror, trains Harry in some dark magic defense techniques that are not taught at Hogwarts. This gives Harry an edge in fighting the dark forces but also makes the Hogwarts faculty a bit wary of him. He could then be in a situation where he has to prove that his knowledge is for good and not for dark purposes.