Triton

Fish man. Merman?

Tritons (not to be confused with tridents) are a race of aquatic humanoids originating from Greek mythology, being followers/descendants of the original Triton, the son and messenger of Poseidon. They can essentially be summarized as "merfolk, but with a sillier name".

In Dungeons & Dragons, Tritons are distinguished from merfolk in that they have two lower limbs rather than one (originally two merfolk-style fishtails in lieu of legs in their 1e Fiend Folio appearance, thereafter changed to the less silly legs with finned feet look) and are more magical; Tritons originated on the Elemental Plane of Water, but have since migrated en masse to the Material Plane, to the point they are considered Native Outsiders in 3rd edition.

Tritons are fairly obscure, but they have been playable races throughout the first 3 editions, getting racial writeups in 1e's "The Sea People", 2e's "Sea of Fallen Stars" for the Forgotten Realms, and 3e's "Savage Species". This is because, unlike merfolk, the tritons' legs allow them to freely move about on land and in the water with equal ease, whereas merfolk are pretty much reduced to crawling like oversized slugs if you pull them out of the water.

AD&D

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3rd Edition

Tritons were with Third Edition from the beginning, appearing in the 3.0e Monster Manual I as a strictly NPC monster type. At this time, they were not among the races to be given level equivalents in the DMG. From there, they were adapted into a fully playable monster class in Savage Species, and finally appeared as an NPC race with a +2 level adjustment in the 3.5e Monster Manual I.

Third Edition Tritons are explicitly described as possessing humanlike legs but still being unable to walk on land; they can move on land only by dragging themselves around like a paraplegic without a wheelchair. Not surprisingly, they weren't a popular choice for player characters and were never given a proper PC stat block (though one could be derived from their Savage Species monster class). 3e players were usually better-off playing an Aquatic Elf, Sea Elf, Sea Kin, Selkie, Aventi, Shoal Halfling, or any humanoid race with the Aquatic template slapped on it.

5th Edition

Tritons are one of the playable races reintroduced to the 5th Edition with Volo's Guide to Monsters. They are very paranoid of other races, having spent the entirety of their lives underwater with little to no contact with the outside world. They act proud and noble, but are like fish out of water on the surface. Almost no-one sees them or cares about what they do, so no one takes their proud boasting about their culture seriously. This can lead to tensions, as your Mary Sue Triton gets humbled by surface dwellers who have no idea who he is.

Forgotten Realms

Statblock

Ability Score Increase: +1 Strength, +1 Constitution, +1 Charisma

Medium size

Speed 30 feet, Swim 30 feet

Darkvision 60 feet

Amphibious: You can breathe both air and water.

Control Air and Water: You can cast Fog Cloud once per long rest. From 3rd level, you can cast Gust of Wind once per long rest. From 5th level, you can cast Wall of Water once per long rest. All spells granted by this trait use Charisma as your spellcasting ability score.

Emissary of the Sea: Aquatic beasts have an extraordinary affinity with your people. You can communicate simple ideas with beasts that can breathe water. They can understand the meaning of your words, though you have no special ability to understand them in return.

Guardians of the Depths: Adapted to even the most extreme ocean depths, you have resistance to cold damage, and you ignore any of the drawbacks caused by a deep, underwater environment.

Eberron

Keith Baker finally and officially merged tritons and merfolk together when he released his Exploring Eberron splatbook for 5e. Rather than being two races which are almost the same save for limbs, the Kalamer are aquatic humanoids who can shapeshift between a legged form, for exploring on land, and a tail-bodied form for better adaptation to life under the water.
To play one, use the Volo's statblock, change the languages to the Eberron appropriate equivalents, and give 'em this extra racial trait:

Kalamer Transformation: When you finish a short rest, you can shapeshift from triton to merfolk form, or vice versa. Triton form functions as per the standard 5e triton. In merfolk form, your legs merge into a large, fish-like tail; your land speed drops to 10 feet and your swimming speed increases to 40 feet. You choose when you adopt merfolk form whether equipment and clothing worn on your legs falls away or is absorbed into your body until you resume triton form.

Scarred Lands

Tritons of the Scarred Lands are the creations of Corean, who tasked them with bringing law and peace to oceans of Scarn. They're divided between the Blood-Tainted Tritons who dwell in the Blood Sea and have been corrupted by the blood of Kadum, and the Clearwater Tritons who dwell elsewhere.

Statblock

Ability Score Increase: +1 Strength, +1 Constitution

Size: Medium

Speed: 30 feet, Swim 30 feet

Amphibious: You can breathe air and water.

Ally of the Ocean: You can convey simple ideas to waterbreathing beasts, and can cast Call Aquatic Beast once per short or long rest. Charisma is your spellcasting ability for this feature.

Ocean's Embrace: You are resistant to cold damage and are not affected by the conditions of a deep underwater enviroment.

Languages: You speak Primordial and one other language of your choice.

Blood-Tainted

Ability Score Increase: +1 Dexterity

Darkvision 120 feet

Claws: You have claws, and can deal 1d4 + Strength slashing damage as an unarmed attack.

Blood Rage: When you take damage in combat, you must succeed a DC (8 + half the damage taken) Wisdom saving throw, that you cna choose to fail, or be overcome by a berserker rage. While in rage you may only attack the creature that provoked your rage. During the rage, you have advantage on attack rolls and deal an addtional 2 points of damage on a successful melee attack, attacks against you have advantage, and you cannot cast spells or maintain concentration. After your enemy is dead, you must make a DC 12 Wisdom saving throw to calm down, and on a failed throw you attack the nearest hostile creature. This continues until you make a successful save, kill all hostile creatures you can percieve, or you're incapacitated. You cannot voluntarily end this rage.

Chameleon: Your skin shifts colors, granting you advantage on Stealth checks.

Clearwater

Ability Score Increase: +1 Charisma

Darkvision 60 feet

Sea's Gift: At 5th level you can cast Control Water, and at 10th level you can cast Conjure Elemental to summon a water elemental, once per long rest. Charisma is your spellcasting ability for this feature.

Triton Weapon Training: You are proficient with the trident, net, and crossbow.

Magic: the Gathering

They are also used in Magic: the Gathering's Theros setting. Here they are much more directly merfolk with legs with a funny name, as they are literally merfolk in creature type. Cosmology isn't particularly related to D&D's as they are not more extraplanar than any other humanoid.

Gallery

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