I wanna make a triton warrior that uses magic related to the sea (think of poseidon powers). Do i just pick eldrichkinght as an archetype or do I multiclass into a spellcasting class? I want them to be an primary melee fighter that uses magic to help them fight.

Look at tempest cleric. Martial weapons, Heavy armor, water and thunder spells. Usually a better caster than melee, but you’ll be good at melee, too. 

If you want a fighter multiclass that works with sea powers, fathomless warlock comes to mind. Or storm sorcerer 

Eldritch knight, your first instinct, can work also. Just trying to throw out other options to explore. 

I love me an Eldritch Knight, but the magic they wield doesn't really scream the grandeur of Poseidon to me. Generally an Eldritch Knight is using buff spells or utility spells and the majority of their casting is cantrips.

 I'm going to second using a tempest cleric, and more specifically one that is built around spirit guardians. I would flavor the spirits as crashing waves where the faces of past triton warriors can be seen coming in and out of form. Something like that.

Spirit Guardian clerics are excellent in melee. Quite scary really. You can still attack every round, and can even make good use of the dodge action. Dodging is one of those things that I think fits the profile of a skilled warrior that rarely gets used by most martials. Meanwhile your Poseidon inspired powers will feel much more like powers and less like minor tricks.

If you're absolutely set on building around an extra attack class, I would go with an Oath of the Ancients Paladin. While the spellcasting is not usually super flashy, smites are. Speak with animals can take your ability to communicate with creatures of the sea to the next level. Nature's Wrath, Ensnaring Strike and Plant Growth can be flavored as kelp or the like. Ice Storm is perfect for adding some weather control to your kit.

 Tritons are pretty naturally set up to make good Paladins already, too.

This is very true. Mechanically and culturally. Tritons sound like paladins when you read their description.

It might not be as optimal but.....maybe you could try a Fathomless Bladelock? It will certainly not be as good as a Hexblade but you can still gain the benefits of the Blade boon Invocations like Thirsting blade, Improved Pact Weapon and Eldritch Smite which are available at 5th level (and Life Drinker at 12th level). You could theme it that your pact weapons are made out of water that you can control the density of to make them function like weapons, or have them be made of ice thematically. You get some cool ocean and storm themed spells.

Like I said, not as optimal as going Tempest Cleric in terms of melee caster but thematically it might make a good option.

Another option is Bladesinger. Full caster with melee and they do get several water, ocean and storm themed spells like Shape Water, Fog Cloud, Thunderwave, Lightning Bolt, Sleet Storm, Tidal Wave, Wall of Water, Watery Sphere, and Conjure or Summon Elemental (water elementals to be exact). 

On a somewhat unrelated note, only Druids get the Maelstrom, Tsunami, and Storm of Vengeance which would be thematically so cool of a Fathomless Warrior or a Tempest Cleric.  

How did I forget about the Fathomless. That's a great idea! Love what you could accomplish with the blade flavoring. Could really feel like a water bender. The spell list fits well and you get the best of both worlds; extra attack and full caster spell progression.

Bladesinger is another elegant solution. Some fire ideas.

And now I want to come up with a solid no wildshape melee druid for this concept that can access those spells. 

GODDAMNIT!!!! I had already made the tempest cleric but you guys are now going to make me try all the other builds.

hehehe. Death by good idea