You can choose any, from Zeus all the way to Priapus. Find out all you can about the demigod. Just keep in mind which ones are famous for not having demigod kids (ex. Hera or Artemis).;
, Maybe Persephone's children can be born from a flower or Hestia's are born from ashes. The possibilities are endless and you can keep adding to and designing your character for as long as you like.
 Work out when they were born, how they got to Camp Half Blood or Camp Jupiter. It's important to understand them completely, including all their flaws and relationships.
 This includes sketching out how they look, what they wear and particular facial expressions. This allows you to picture the character better. Moreover, if you're adding them into a story, it'll be easier to explain how they look.
 Each demigod has a worst enemy equivalent, such as Luke, Kronos, and even Gaia, so start gather up the characters and work out which one would be their worst enemy. This enemy could also shape your character, maybe they caused a wound or killed someone they loved. This adds effect and makes your character more interesting.
 Every demigod has a weapon, even if it's a saucepan. Maybe their weapon is cursed or used to be used by a famous hero (for example, Hercules). Their weapon doesn't have to be enchanted at all, maybe they just use their powers, such as water, or whatever powers they have that are related to their godly parent. Then again, it could just be a knife that doesn't need to be enchanted.
 Hades' children don't have to be all gloomy; try making them happy, this way your character is different from the others. Sometimes making them like their parents is useful though, such as using Hermes' craziness or Hecate's weirdness.
 Keep in mind what is in actual Greek or Roman mythology, and what it in the books.
Research a particular god or goddess as your starting point.
Don't worry if they're virgin or already in a relationship.
Go in depth into your character.
Draw up a rough copy of your demigod.
Select an enemy for your character.
Choose a weapon for your character.
Don't hesitate to make your demigod totally different from their parent.
Continue developing the demigod character.
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