Obviously, Percy Jackson himself is very common. Since the fanfiction is centered around him having godly strength, he's the main focus. Annabeth Chase also frequently appears as she's Percy's close friend and love interest. Grover, Percy's satyr friend, is another common character as he often gets involved in Percy's adventures.
His godly strength can be shown through physical feats like lifting extremely heavy objects with ease, such as entire buildings or large boulders. He could also be depicted as having super - fast running or swimming abilities, outpacing even the fastest demigods or sea creatures.
Percy Jackson himself is very common, as the main character of the original series. Writers often like to put him in new and chaotic situations.
One interesting plotline could be Percy using his newfound godly strength to take on ancient and powerful monsters that were previously too strong for him. For example, he might face a primordial being and have to find creative ways to use his strength to defeat it.
Grover can play a role too. Although he is Percy's best friend, in some fanfictions, there could be a situation where Percy gets jealous if Grover spends more time with Annabeth on a quest or if Grover seems to have a closer bond with her in a particular situation. It's not as common as Percy - Annabeth or Percy - Nico scenarios, but it can add an interesting twist to the fanfiction.
In a lot of Percy Jackson God harem fanfiction, Percy is the central male figure. As for the female characters, Aphrodite is a popular choice because she can bring in the aspect of love and attraction, which is key in a harem - like story. Athena is also common because of her intelligence and power. She can create an interesting contrast to Percy's more impulsive nature. Additionally, Hestia is sometimes included. Her calm and nurturing nature can add a different flavor to the harem dynamic.
Annabeth could potentially be a yandere in some fanfictions. Since she already has a strong connection with Percy in the original series, some fanfic writers might take that to an extreme, making her overly possessive. Another could be a new, made - up character. Maybe a demigod who has been watching Percy from afar and then develops an unhealthy obsession.
Percy himself is obviously very popular. After all, it's his series. Annabeth is also a fan favorite, as her intelligence and strong will make for interesting storylines. Nico di Angelo is quite popular too, especially when his powers and his somewhat dark nature are explored in fanfiction.
Another common opponent could be other demigods from different cabins. For instance, a child of Ares who might have a more aggressive and straightforward fighting style compared to Percy. This would create an interesting dynamic as they have different powers and personalities but are still on the same side in the general scheme of things.
Monsters from Greek mythology are also very common. Giants, like the ones Percy faced in the original series, are frequently used. They are powerful and require Percy to use his water - based powers in creative ways to take them down. It's a classic type of fight that fans love to read about.
Percy is definitely one of the most popular. His powers and his relatable, humorous personality make him a natural choice for fanfiction. Annabeth is also very popular as she is intelligent and strong - willed. Her strategic thinking can add a lot of depth to the gaming - related stories.