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When Akatosh manifests late in the 3rd ERA at the end of the Oblivion Crisis, he takes the form of a dragon. He is also known as the Dragon God of Time. A Dragonknight's draconic skill tree seems consistent with Akatosh's draconic link.
The templar class and its abilities, the whole aesthetic of it reminds me of the ending of Oblivion and Martin's transformation into Akatosh. So I vote templar
Akatosh has "dominion" over the sun, depending on the player's view of it (Elder Scrolls lore is purposefully made so that you only get unreliable "truths", so that players can see it from their point of view). In some cultures he is shown as holding the sun. As Auri-Ell, in Skyrim, you get a bow that channels power from the sun.
With that said, the Templar uses bright sun like abilities. Radiant glory, sun fire, solar flare....etc. While I do think those that said Dragon Knight have some very good points, I think Templar best represents Akatosh.
Dragon Knight - These skillful masters-at-arms use the ancient Akaviri martial arts tradition of battle-spirit, and wield fearsome magic that pounds, shatters and physically alters the world around them. -ESO
Templar - These traveling knights call upon the power of light and the burning sun to deal massive damage to their enemies while restoring health, magicka and stamina to their allies.
"Krist the Lionheart? No. Lionheart was my dog" -Krist "Darling, if looks were everything, I would be king of the world" -Luke
"That place, between day and night, that purple color just before dark, that is where you will find me"- Hughe
From a lore/background perspective its 100% templar. As someone said the description of the dragon knight class tell us they are trained in the akaviri martial arts, and I remember reading a book telling us a similar story, how DKs were trained by one of the last dragonguard leaders; Now the templar skills are described as "divine", not being specific so you can decide what is your "patron" god. That being said, DKs do have a nice draconic feel to them, so it depends on what's more important to you: the lore or the looks (and besides, there is nothing preventing you from being a disciple of akatosh that is also trained in the akaviri martial arts ).