Brainstorming here, so apologies for being somewhat stream of consciousness.
If arcane is traditionally held to be in opposition to divine, than it makes sense that the arcane half-caster would be in opposition to the paladin, which is an extremely strong trope with tons of identification as the "divine warrior".
So aesthetically, the paladin is very much tied to sword and board, heavy armor, mounted knight visualizations. Themes of faith, endurance, and protection, lots of radiant light imagery. So let's reverse it, but stay on a warrior thematic without going full dark knight.
No shield, no armor. Dueling weapon or big weapon. Protected by skill and magical potency, not armor. Evades, parries, and counters, doesn't endure big hits. (Trope precedent: Avenger, bladesinger. Contrast with spellsword, abjurant champion, possibly heavy armor/Str as subclass theme.)
Weapon possibly imbued or empowered by arcane energy (Precedent: Black blade magus, swordmage, hexblade warlock). Magic focused on mobility, aggression, spell strikes with weapons. Haste a must (Precedent: 3.5 swiftblade). Paladin heals and protects, AHC is more offensive, but still has some support. Focus on elemental, force, dimensional spells (Precedent: swordmage).
Paladin leans lawful good (as a trope), AHC leans towards chaotic. Liberator and seeker, as opposed to protector and champion. Like paladin, warrior first, caster second. Thematic of warrior who has some innate magic because of their natural talent, not a mage who has bent their magic towards fighting. Bladesinger, sword bard, hexblade already have "caster who picked up fighting tricks" trope covered.
Possible subclasses: Templar (anti-magic/magebreaker), Enhanced (imbued with magic, possibly against their will), Swiftblade (focused on mobility and teleportation).