Jacaerys Velaryon
Rhaenyra's eldest, heir after his mother, rider of Vermax — brown-haired where Velaryons run silver, and made to carry the court's whispers about it. Earnest, dutiful, and better than the war deserves.
The fuller tale
Rhaenyra's eldest son by Laenor, and heir to her claim after her, Jacaerys grows up carrying two burdens at once — the weight of being second in line to the Iron Throne, and the weight of a court that never stops quietly discussing his brown hair in a family where every other Velaryon and Targaryen runs silver-blond.
Rider of the dragon Vermax, Jace is, by nearly every account in both tellings, more earnest and more dutiful than the war he is born into deserves — a boy who takes his responsibilities seriously at an age when most of his cousins are still permitted to be children, precisely because his mother's claim and his own legitimacy cannot survive him being anything less than exemplary.
As the Dance escalates, Jacaerys becomes one of the black cause's most active young commanders and messengers, flying Vermax across the realm to rally bannermen, negotiate with wavering lords, and do the unglamorous diplomatic labor that keeps his mother's fractured coalition from falling apart entirely.
His mission eventually takes him to the war's naval front, where the Triarchy's massed fleet in the Gullet poses one of the black cause's most serious external threats — a battle that asks considerably more of a young dragon and an even younger commander than either has yet been tested against.
The page and the screen
Jacaerys receives substantial development in the show's aired seasons as one of Rhaenyra's most sympathetic and competent children, his diplomatic missions and his relationship with his siblings given considerable screen time. Fire & Blood treats him with similar respect but far more economy, recording his various missions and his death at the Gullet in the compressed, matter-of-fact register the book reserves for even its most consequential losses.
In the show, season by season
Season One. In The Black Queen — Sworn to win his mother the mountain and the snow.
Season Two. In A Son for a Son — Wins the North with honesty, then hears about Luke. In The Red Sowing — Won the North with his name; watches the name matter less by the hour.
Where they stand, season by season
Their fate — if death has found them, it is written here. Open at your peril.
The books: Lost with Vermax in the Battle of the Gullet (F&B, ch. 5)
In the Battle of the Gullet the queen's heir flew Vermax too low among the Triarchy's ninety ships. Dragon and prince went into the sea; the Myrish crossbows found him swimming. With him drowned the best of the blacks' next generation.
The series has not yet reached the Battle of the Gullet; Jacaerys's fate remains ahead of the current seasons.
Fire & Blood places his death in that battle, where the queen's heir flies Vermax too low over the Triarchy's massed warships during the fighting. Dragon and prince are brought down together into the sea, and Myrish crossbowmen find Jacaerys swimming before he can reach safety, finishing what the fall into the water started. With him, the book notes bluntly, drowns the most promising of the black cause's second generation.