Poseidon's children have power over the ocean and some freshwaters, earthquakes and horses.
She had none, she was a virgin goddess.
When a god marries a demigod the demigod receives the same powers as the god. Which makes the demigod now more powerful the god. So the demigod has their powers and the powers of the god.
The Power Of Zeus Children is the power to throw lighting bolts.
The Greek goddess Artemis was a virgin goddess, so she had no children. If she did have a demigod child, her/his powers would be similar to Artemis'. They would probable be able to shoot an arrow with perfect aim and heal.
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No, Hestia did not have any demigod children, she was a virgin goddess.
No she does not.
No, Perseus was a mortal. actually Perseus was a demigod (half god and half mortal) his father is Zeus and mother is Danae(a mortal)
No. Since Artemis is a virgin goddess, she can't have any demigod children.
No, Hades has no children.
Yes, a Hero in greek mythology was cosiderd as a mortal or human that had extordenary powers or was an offspring of a God-Mortal, DemiGod-Mortal or God-DemiGod and inherting powers by a godly gen of one of the parents making their powers relevent.
Hera's children had diverse "powers". She being the goddess of family and marriage, she wouldn't have bastard children, and her only children are, therefore, also children of Zeus, thus being Gods. Hera's children were: Ares, Enyo, Hebe, Eilethya, Hephaestus, and Eris. Ares was the God of war, Hephaestus, was, according to Wikipedia, the god of blacksmiths, metallurgy, fire, volcanoes, technology, among others. Eris was the goddess of discord. As you can see by these examples, Hera's children all had different specialities and different powers, and therefore, we cannot say Hera's children had a certain "kind of power". Either way, if you are asking about the Percy-Jackson-demigod-kind-of-power, Hera didn't have demigod children because of the reasons listed above.