I'm not sure about a specific 'Percy son of Zeus and Hera fanfic' that stands out above all others. However, you can try looking on fanfic platforms like Archive of Our Own. There, you can search for this specific type of fanfic and read the reviews to find a really good one. Usually, the ones with high ratings and a lot of bookmarks are worth checking out.
One common theme is identity. Since Percy is suddenly the son of Zeus, he has to figure out who he really is. Another theme is power. With Zeus as his father, he may have new and greater powers to control.
Power and responsibility are often themes. Percy being the son of two major gods has a great deal of power, and he has to learn how to use it responsibly. Also, acceptance is a theme. He has to gain the acceptance of the other gods and demigods who may be skeptical or even hostile towards him at first.
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.
The plot could revolve around Percy's relationship with his divine parents. Since Zeus and Hera have a complex relationship themselves, Percy might struggle with their expectations. Maybe he's caught in the middle of a power struggle between Zeus and Hera's different ideas of how he should use his powers. He could also be trying to unite the camps of different god - related demigods under his leadership as the son of two major gods.
One possible plot could be Percy's journey to discover his true place among the demigods. Since he is the son of Leto and Zeus, he might face unique challenges. For example, he could be caught in the middle of power struggles between different camps of demigods. He may also have to deal with the expectations and rivalries that come with having such powerful parents. His powers, which could be a combination of those associated with Leto and Zeus, might make him a target or a valuable ally.
A great antagonist could be a Titan who has a grudge against Zeus and sees Percy as an easy target to get back at him. For example, Atlas. He could try to use Percy to free himself from his burden again or trick Percy into doing something that would cause chaos among the gods. Another option is a powerful and vengeful demigod who feels that Percy, as the son of Zeus, has been given too much power and attention, so he wants to take Percy down.
One popular 'Percy son of Zeus fanfic' is 'The Lightning's Heir'. It has an interesting plot where Percy, as the son of Zeus, discovers new powers and goes on a journey to save Olympus from a hidden threat.
The Titans could be the main antagonists. Even though they were defeated before, they might see Percy as a threat because of his powerful parentage. They could try to stop him from fulfilling a prophecy or gaining more power. For example, Kronos might have some remaining influence and try to manipulate events to destroy Percy.
His powers might include the ability to control the weather like Zeus. So he could summon thunderstorms or clear skies at will. From Leto, he could inherit a connection to the moon. This might give him enhanced senses during the night or the ability to draw power from moonlight. He could also have some form of protection or blessing related to his mother's association with motherhood and fertility in mythology.