Inspired by Critical Role I decided I wanted to create my own campaign setting world, my fiance also became interested in D&D through CR and wanted me to create an Elf tiefling race (we decided to name them Elflings) for her to play, I was wondering if anyone here had any thoughts and ideas on how to go about executing that creation, please don't comment (just make a tiefling and say they're half elf) if I wanted that, that's what i would have done, I want to create a balanced mix of those races that would be fun to play, without making them over powered, I dont want the players to be incentivised to only pick the OP race, all thoughts and ideas welcomed :) 

I would consider using half-elves as a guide.  The various sub-types of half-elf can each select a trait from their elven parent; that seems a good place to start.  Make the 'Elflings' +2 Dex, +1 Charisma, give them darkvision and fire resistance, and whichever inheritable 'Elf' trait corresponds to the character.

The real kicker is that half the elf's traits are due to their Feywild heritage and fey-tinged blood, which kinda directly clashes with the idea of Infernal heritage instead.  I would not give these devil-elves trance, and Fey Ancestry seems to cut against the grain a bit.  Hm.  Keen Senses may fit, as both elves and devils are known for superior vision (actual Keen Senses for elves, Devil's Sight for devils), but it also kinda feels like a copout.  Perhaps a reseasoning, of sorts, for Ancestry.

"Volatile Heritage: Your deeply mixed blood carries the power of both fiend and fey, granting you supernatural resilience.  You have advantage on saving throws against being charmed and magic cannot put you to sleep.  In addition, you count as both an elf and a tiefling for the purposes of acquiring race-specific feats."

So the full list would be:
ASI +2 Dex / +1 Cha
Fire Resistance
Galactic Standard Darkvision
Parent Elf Trait
Volatile Heritage
Basic Languages (Common and choice of Elven or Infernal, or just all three if you're feeling generous)

Leans more elf than tiefling, but you get arguably the best tiefling trait and you don't get the best elven trait(s), so seems reasonably in line?

I would do it this way:

ASI: +2 Cha, +1 Dex (Both Half elf and Tiefling are +2 Cha)

Darkvision

Their Choice of:  

• Immunity to (Charm and Sleep) and their choice of one of the various Tiefling Legacies  (Infernal Legacy, etc.)
• Fire Resistance and their choice of one of the various Half Elf Legacies  (Swim Speed, Elf weapon, Drow Magic, etc.)

Languages:  Common and their choice of Elven or Infernal

I would take the +1 dex +1 charisma and +1 intelligence or wisdom. Then give them the choice of fire resistance or charm and putting to sleep. Then change up the infernal legacy to: thaumaturgy or druidcraft, entangle or hellish rebuke and darkness or misty step. Darkvision is a must. Maybe give them elven weapon training? 

It doesn't look like anybody's mentioned this, but such a race has existed in D&D for a while. You're looking for "Fey'ri", which is named by a stupid combo of fey and tanar'ri (demon). You can find the 3e version of the fey'ri in Races of Faerun, and the 4e version in Dungeon magazine 208. Fey're had the following stats in 3e:

• +2 Dexterity, +2 Intelligence, –2 Constitution
• Medium-size
• 30 ft walking speed, but some have wings with 40 ft flying
• 60 ft darkvision
• Immunity to magic sleep spells and effects
• +2 racial bonus on Will saves against enchantment spells and effects
• Access to the alter self spell at will
• A +2 racial bonus on Bluff, Hide, Listen, Search, and Spot checks.
• Fey'ri are considered elves for requirements, and also naturalized outsiders (like a fiend in this case)
• Access to four of the following: (spells are once per day): charm person, clairvoyance, damage reduction 10/+1, darkness, detect thoughts, dimension door, enervation, fire resistance 10, suggestion, +2 bonus on saves against electricity, or +2 bonus on saves against poison

And the fey'ri had a level adjustment of +2 to +3 depending on the last ability, meaning that a level one fey'ri would be as powerful as a level three or four character of a standard race. All of these would clearly be overpowered in 5e, especially the flight and spells.

In 5e I think you're all on the mark. Bonus to Dex and Int, darkvision, fey ancestry, and a choice of some of the spells above or resistance to either fire or poison. Easy on the spells there. Ignore the flying and outsider bit. They're still humanoids (as with tieflings).

Yeah use half elves and just replace the human traits for tie fling and give it a tie fling name

So Im trying to do this but I can't figure out how to find fey'ri on dndbeyond. It says can't be found. So how do you make this character? Is it one of the things you have to buy?

It's not official content, so people had to homebrew it. You might find it in published homebrew races. Otherwise, you can homebrew one yourself using the homebrewing tools.

Actually put the term in the filter for you here.  You probably want to pay attention to the ones that are actually adopted by users.

Just to let you know, there already is  a race for half elf -half tieflings they are called Drya'boli 

Quote from eclipse_cat666 >>

Just to let you know, there already is  a race for half elf -half tieflings they are called Drya'boli 

 But that’s homebrew. Also hello fellow cat person.