#arethousa

So for LOOKS first:

Since the Hesperides are goddesses nymphs of evening and (the golden light of) sunsets; so which give colours of golden, red/orange, black, and navy blue.

So for typical hair colours, I can imagine a child of the Hesperides having hair that is either golden (either very pale hair that looks white to actally blonde hair) to represent the yellow hue of the sunset and the sun, auburn (definitely red in hue) to represent the dawn/rose coloured epithets of Eos, or black like the night. As for eyes, they could either have blue eyes for the general sky, or brown-amber eyes to represent the golden sun. But of course, if Percy can have sea-foam green eyes well, a demigod of the Hesperides can have an eye colour that is slightly atypical.

Now PERSONALITIES:

I can see the child of Hesperides being generally aloof to represent the Hesperides being generally secluded by themselves from others so they're not used to or not as open faced. However, they are less aloof and show more emotional to their families and close associates who they share strong bonds with.

Once they are open/warmed up to others, their seemingly aloof exterior is bright and have hues of personalities much like the colours of sunset so its jist a matter of time

They have a desire or affinity for care taking, managing, and protecting; much like the the Hesperides in their role taking care of the Golden Apple Tree of Hera, and the treasures of the gods. They are also very defensive of their belongings and others, ranging from reluctant to lending out their stuff to others to doing their best to prevent others from touching it.

Otherwise, those are just personalities that they would inherit as a "Hesperides".

Powers-Wise, I wanna say definitely something they might both have light and darkness powers but minor in both. Nothing like a child of Apollo/Helios or a child of Hades, and power-level scale wise and technicalities and possibilities, they are below them, but they make up for it for having both light and darkness elemental powers at their disposal. They might lean to one more than the other in strength, talent, and just in general what they prefer based on the individuals' personality and attribute, but doesn't change that they can still use both.

So basically, they can use light and darkness powers to cast light and darkness and manipulate it when they need to, but they can't like cause a powerful bolt of light like Will can or shadow travel like Nico. They could try or pull it off once in times of desperation like a Hail Mary, but with severe repercussions.

The child of Hesperides is a child of the evening and golden light nymphs afterall, and half-mortal.

Another power the child of the Hesperides could have is the "power of sweet song". The Hesperides have been noted to have this and have sung many times especially as Heralds of Bridal Nights (Short version: they were notably written singing at the wedding of Thetis).

Now what this power of sweet song details, it could mean anything. Could they have a silver tongue that they can beckon others to do what they want? Do they have the power similar to a siren where they can hypnotize/enchant others? Something like Charmspeak but not really? Who knows! but its definitely allows room for what is convinent to you.

Definitely they have the qualities of a child of Apollo where they can use their music, in this case for the child of Hesperides is their voice, to sing to create an effect.

They might have minor water abilities as the Hesperides were referred to as daughters of Oceanus as stated in the Argonautica but that's a stretch if you go with the PJO canon that they are a children of Atlas.

Now for some extra details is depending which of the Hesperides the child is of, it can affect some things.

There are four notable Hesperides that pop up (although I think they are like 7? off the top of my head) but each of their names mean something that can be used to your advantage like AIGLE "The Radiant", ERYTHEIS "The Red", HESPERE "The Evening", ARETHOUSA "War-swift".

Alto, if you're talking about this child of Hesperides whose mother is Erytheis 'The Red', like that one previous ask, you could have their light being red in colour, reflecting Erytheis's name and quality, and having red hair as such. Or maybe they have red eyes. In the Apollonius Rhodiaus Argronautica, thanks or persuaded by Orpheus, Erytheis became an Elm tree which you can use to your advantage. There's also some minor connection with Erytheis noted son Euryton, who was associated with herding, which maybe a better communication with Satyrs for the child of Erytheis.

If its Aigle 'The Radiant', this child of Hesperides definitely leans more to Light powers more to reflect the "Radiance" of their mother, and may inherit their mother's gentle voice (as mentioned in the Argonautica). Aigle became a Sacred Willow when rising out of the dust in the Argonatuica. Which you can use qualities of Willow for this child. Maybe they have long hair like a willow or have a 'healing' side to them, since Willow has been noted in Folk Medicine to have healing back to Ancient Egypt and Greece, and Willow itself is a robust tree that was used in daily life; so maybe they're a handy person or a person of many talents.

If its Hespere 'The Evening', they have more darkness and night powers more as part of the "Evening". Hespere/Hespera became a Poplar tree in the Argonautic, but you could make them popular because well, poplar and popular sound kind of similar to each other. There's also some potential connection with Venus※ or even the Horae Hesperis ('Evening': the 10th Horae/Hour who presided over the hour of dusk), with the name connection. ※(Side Tangent: Long story short, there's another god named Hesperus, son of Eos/son of Iapetus and brother of Atlas, and who is supposedly the father of his daughter who is also named Hesperis (which is also a floral plant IRL), who with Atlas gives birth the Hesperides. Hesperus is also the Evening star, the planet Venus in the Evening. How this works in the Riordanverse, I dunno but its there for you if you want to go down that rabbit hole).

If its Arethousa 'The Warswift', their personality is more bold, passionate, and quick to act as one whose mother is warswift. Take some fitting attributes that are similar to a child of Ares, mostly because of "Are" in Arethousa, or even children of Nike to them but without, the iconic stuff that is iconic to children of Ares (blood) and Nike (victory). Maybe they are swift like a shooting star kind of deal. Basically, Arethousa could have a war god attributes, due to her name, but isn't really a war god, and their child could have similar qualities with other war god demigods.

There's also a fact that the Hesperides as caretakers of the treasures of the gods and there have been heroes (i.e. Perseus) who borrowed them in his quest, and there is a possibility the child of Hesperides may be allowed to use one of the treasures as their time as a demigod, but the stipulation is, they are simply borrowing it because all that is under the care of the Hesperides are eventually given back to their hands; from the golden apples and the treasures that Perseus used against Medusa.