His powers would likely be much darker. He might have the ability to manipulate shadows like Nyx, using them to hide or even attack. And from Tartarus, he could have the power to cause earthquakes or open up chasms in the earth. He could also have a natural resistance to the harmful effects of the Underworld, such as the poisonous gases and the draining of energy that normal demigods experience.
His relationship with Annabeth would be very different. Annabeth might be initially scared of Percy because of his dark lineage. She would be cautious around him as she is used to the more 'typical' demigods. Percy, on the other hand, might feel isolated from her because he knows she is wary. His friendships with the other demigods at Camp Half - Blood would also change. Some might avoid him, while others might be intrigued by his new powers and origin. Grover, for example, might be torn between his loyalty to Percy and his fear of what Percy could become.
His powers might become more related to the night. He could gain the ability to see clearly in the dark, like having night vision. Maybe he could also manipulate shadows, using them as a form of defense or offense. For example, he could create shadowy constructs to fight his enemies.
His water - based powers might become corrupted. Instead of just controlling clean, life - giving water, he could now also manipulate dark, poisonous waters from the depths of Tartarus. This would make his powers more dangerous but also more unpredictable.
His water - based powers might intensify as he is in a place filled with so much negative energy. He could learn to control the strange, dark waters in Tartarus, which are probably more powerful and unpredictable than normal water. Maybe he can use them as a shield or a weapon in ways he never thought of before.
If Percy was the son of Gaia and Tartarus in fanfiction, his power set would be a fascinating blend. From Gaia, he could potentially have the power of terraforming, reshaping the earth on a large scale. He might also be able to communicate with all forms of earth - bound life. From Tartarus, he could gain the ability to traverse the darkest depths of the underworld with ease, and perhaps even draw power from the primordial chaos there. This would make him a very different and much more complex character compared to his original form in the official series.
Well, Percy's new powers could include the ability to communicate with creatures of the night in a way he couldn't before. Maybe he could call upon the help of shadowy beasts or entities that are associated with Nyx and Erebus. His strength might also be tied to the level of darkness around him. In a pitch - black place, he could be extremely powerful, while in bright sunlight, his powers might be somewhat weakened.
In this fanfiction, Percy would likely have powers related to both Apollo and Athena. Canon Percy has water - based powers from Poseidon. But here, he might have the ability to heal like Apollo, which would be a huge difference. He could also have enhanced intelligence and strategic thinking from Athena. So instead of just relying on his strength and water powers in battles, he could use his wits and healing abilities as well.
His powers would likely be much more elemental. Since Ouranos is associated with the sky, he might have powers over the air, such as creating powerful winds or even controlling the weather on a greater scale than before. And from Gaea, he could have enhanced earth - based powers like causing massive earthquakes or having a deeper connection to the land, perhaps being able to communicate with all forms of plant and animal life that are rooted in the earth.
His powers would be much more extreme. Instead of just controlling water like he does as a son of Poseidon, he could control light and air elements. His connection to Aether could give him the ability to manipulate the very fabric of the upper atmosphere. And from Hemera, he might have the power to bring instant daylight or even manipulate time related to the day - night cycle.
His powers could be more nature - based. For example, instead of just controlling water, he might be able to control all forms of liquid in nature, like sap or blood. His connection to the wild could also make him more attuned to the emotions of animals, allowing him to communicate with them more effectively.