Matthos Seaworth
Davos's eldest son, devout in the red god's new faith and proud to serve aboard his father's ship in Stannis's fleet.
The fuller tale
Matthos is what the second generation of a self-made man looks like: raised on the respectable side of his father's knighthood, lettered, earnest, and a little embarrassed by Davos's caution. He serves aboard his father's ship in Stannis's fleet and burns with two faiths at once — in the Lord of Light, whose new fire has caught the young men of Dragonstone the way new fires do, and in Stannis's cause, which Matthos holds to be simple justice. His father believes in neither god nor king so much as in weighing costs; their arguments about it, gentle on both sides, are the tale's small portrait of a family crossing from one class into another in a single generation.
He wants his father to be more than a knight — to stand on his rights, to take the god seriously, to believe the war is holy. Davos wants his son alive. The Blackwater settles the argument the way the story settles most arguments about faith and fire, which is with fire.
The page and the screen
In the books Matthos is one of seven Seaworth sons and not the eldest — Dale captains a ship of his own, and four brothers sail into the Blackwater together. The show, keeping only Matthos, concentrates the family's whole devout younger generation into him, and gives him the R'hllor fervor that the books distribute more thinly. Either way he serves the same narrative office: the cost of the Blackwater written on Davos's face for the rest of the story.
Where they stand, season by season
Their fate — if death has found them, it is written here. Open at your peril.
The show: Fell on the Blackwater (S2·E9)
The books: Lost on the Blackwater (ACOK, ch. 58)
Davos's devout son sailed beside his father into Blackwater Bay, sure the Lord of Light would deliver the city. The wildfire took his ship whole; the smuggler's luck that saved Davos found nothing of Matthos.
He died where his faith told him victory waited. Sailing with his father into Blackwater Bay, sure the Lord of Light would deliver the city to the rightful king, Matthos was aboard when Tyrion's trap sprang and the river ignited. The wildfire took the ship — in the books, the fleet's whole van, four Seaworth brothers among the thousands — and while the sea gave Davos back, battered onto a spur of rock in the bay, it never gave back Matthos. In both tellings his father surfaces from the green fire having lost the argument he most wanted to lose: the god his son trusted either wasn't watching, or was.