They could interact in many ways. For instance, Percy's younger brother might be a devotee of Zeus and constantly seek his guidance. Zeus, in turn, could use the younger brother for his own purposes, like having him perform tasks that Percy would refuse.
In fanfiction, Percy's younger brother could be a mediator between Percy and Zeus. Since Percy sometimes has a rocky relationship with Zeus, the younger brother could try to smooth things over. He might use his charm or some special ability he has to bring the two together, creating a more harmonious situation in the fictional world.
Well, the younger brother could start off on the wrong foot with Zeus. Maybe he accidentally offends Zeus in some way, and then has to go on a journey to make amends. Along the way, he discovers things about himself and his relationship with Percy. It could be a really engaging story arc in the fanfiction.
The character of Percy's younger brother in Zeus fanfiction could bring new dynamics. He could be a source of conflict, perhaps being jealous of Percy's achievements and trying to outdo him in the world of the fanfiction. Or he could be a support, working alongside Percy against common enemies. It all depends on how the author wants to develop the character.
In this fanfiction, a great plot twist could be related to Percy's origin. What if Percy wasn't really born in the normal way as a god's offspring? He could be a product of some ancient magic that Zeus unknowingly participated in. This revelation could shake the very foundation of the relationship between Percy and Zeus. Also, Percy might discover a hidden side of Zeus' past that Zeus has been trying to keep secret. This knowledge could put Percy in a dangerous position as he decides what to do with this information, whether to expose Zeus or keep it to himself for the sake of their relationship.
In some fanfictions, Zeus interacts with Percy in a hostile way at first. He sees Percy as a threat to his power and the order of Olympus. For example, he might try to limit Percy's abilities or send challenges to prove Percy's unworthiness.
One possible plot could be Percy, as the brother of Zeus, having to deal with the politics of Olympus. He might struggle to find his place among the other gods while also trying to use his powers for good. Maybe he teams up with some of the younger demigods to bring about change in the rather old - fashioned ways of the Olympian council.
Fanfiction often takes creative liberties. In this case, it might be that the author wanted to explore new power dynamics and character interactions. If Percy was Zeus' brother, it would completely change the power balance in the world of the series. Percy's connection to the sea and Zeus' control over the sky could lead to all sorts of interesting plotlines, like joint quests or power struggles between the two 'brothers'.
The other gods would probably be very cautious around Percy. Since he's Zeus' younger brother, they would fear that any wrong move towards Percy could anger Zeus. For example, Poseidon might be more respectful towards Percy than he would be to an ordinary demigod, as he wouldn't want to create a rift with Zeus over Percy.
Well, one possible plot could be Percy discovering he's Zeus' brother in a very unexpected way. Maybe through some ancient prophecy that was long forgotten. He'd then have to deal with the power struggles within the Olympian family, as well as his own identity crisis. Another aspect could be his relationships with other demigods changing, as being related to Zeus is a huge deal.
The main antagonists could be some of the more traditional and power - hungry gods. For example, Hera might see Percy as a threat to the order she has maintained for so long. She could try to undermine him at every turn, fearing that his new ideas and his relation to Zeus will disrupt her plans. Another antagonist could be Ares, who might be jealous of Percy's potential power and influence over the other gods and demigods.
Another possibility is that Percy discovers some long - forgotten weakness of Zeus. In the world of fanfiction, the author could create a scenario where Percy stumbles upon an ancient prophecy or a hidden secret about Zeus. This knowledge could give Percy the upper hand. He could then use his wits and his powers to exploit this weakness and defeat Zeus.
In the fanfiction, Percy's relationship with Zeus may develop gradually. Zeus, being a powerful and often aloof figure, might initially be distant from Percy. But as Percy shows his courage and abilities, Zeus could start to take a closer interest. This might lead to Zeus mentoring Percy in some ways, teaching him about godly powers and responsibilities.