Genasi as presented in the D&D 5E Princes of the Apocalypse campaign book were extremely varied in the traits available to the sub species. The version presented here is largely inspired by the format of Tieflings and their variants, with a cantrip and a low level spell like ability. Additionally each sub-race has its own elemental resistance or similar.
This material was put together while we were running that campaign at our table and is intended to supplement the original material. May it fit the needs of your particular table!

Genasi are born from the influence of the Elemental planes. This may derive from an ancestor who was a dao, being born near a planar gate, the influence of a Primordial being, or some other surge in elemental power that fundamentally changes them.

To the casual observer, the individual Genasi may appear as any other humanoid race with a slightly different hue of skin but their very nature has been altered. For those seeking to inject style into the mechanics of the race, It is encouraged that this elemental nature reveal itself when the special abilities are used of other narratively appropriate moments (e.g. emotionally charged with anger or fear or joy), because it looks cool when the fighter’s hair appears to ignite or winds begin to blow when the mage walks into a room.

… because style over substance look cool!

ALL GENASI

  •   Ability Score Increase. Your Constitution score increase by 2
  •   Age. Genasi mature at about the same rate as most humanoids, though they do live somewhat longer.
  •   Alignment.  Independent and self-reliant, genasi tend toward a neutral alignment though they are not restricted to it.
  •   Size. Genasi are size medium, displaying the same range as other humanoids.
  •   Speed. Your base walking speed is the same as other humanoids, typically 25 to 30 feet.
  •   Languages. You can speak, read, and write Common and Primordial. Primordial is a guttural language, filled with harsh syllables and hard consonants. You are fluent with the Primordial tongue of your associated element (Auran, Terran , Ignan, Aquan) and halting if attempting to speak another.
  •   Elemental Abilities. As a genasi, you possess a certain degree of control over a specific element.
  • Subraces. Four major sub-races of genasi are found among the worlds of D&D, air, earth, fire, and water genasi. Choose one of these sub-races.

AIR GENASI

  • Ability Score Increase. Your Dexterity increases by 1.
  • Unending Breath. You can hold your breath indefinitely while you are not incapacitated.
  • Lightning Resistance. You are resistant to lightning damage.
  • Air Mastery. You know the cantrip gust. Additionally, at 1st level you may cast feather fall. You regain the use of this ability after a long rest.
  • Warding Winds. At 3rd level, you may as an action create a 10 foot radius of warding winds. This effect requires concentration and may last up to 10 minutes. While it is active:
    • ranged attacks that pass through the radius are at disadvantage
    • movement for creatures other than you within the radius is treated as if it were difficult terrain
    • gases, vapours, and other effects that can be dispersed by strong winds are pushed away
    • This ability is regained after a long rest.

EARTH GENASI

  • Ability Score Increase. Your Strength increases by 1.
  • Earth Walk. You may move across difficult terrain of earth or stone as if it were normal terrain.
  • Skin of Stone. You take 1 less damage from bludgeoning damage.
  • Earth Mastery. You know the cantrip mold earth.
  • Stone Fist. At 3rd level, as an action you can draw upon the might of the earth. This ability requires concentration and lasts up to 1 minute. For the duration, your unarmed attacks now deal 2d6 bludgeoning damage. If using a melee weapon, you may add 1d4 to the weapon damage instead.  Strength checks are at advantage but your movement rate is reduced by 5 feet. This ability is regained after a long rest.

FIRE GENASI

  • Ability Score Increase. Your Intelligence increases by 1.
  • Dark Vision. You can see in dim light as if it were bright light for up to 60 feet. Similar to dark vision but instead of seeing things in shades of black and white, you see them in shades of red.
  • Fire Resistance. You are resistant to fire damage.
  • Fire Mastery. You know the produce flame cantrip. Once you reach 3rd level, you can cast burning hands as a 1st level spell. You can use this ability again after a long rest.

WATER GENASI

  • Ability Score Increase. Your Wisdom increases by 1.
  • Acid Resistance. You are resistant to acid damage.
  • Amphibious. You can breathe air and water.
  • Swim. You have a swim speed equal to your land movement.
  • Water Mastery. You know the shape water cantrip. Additionally, at 3rd level you can cast create or destroy water as a 2nd level spell slot, affecting a total of 20 gallons. You regain this ability after a long rest.

Looking for a pretty PDF format for this? It was put together as a Pay What You Want on Drivethru RPG as well!