In the Player's Handbook (PHB, p. 42), it describes the regular Infernal Legacy trait as follows:
You know the thaumaturgy cantrip. Once you reach 3rd level, you can cast the hellish rebuke spell as a 2nd-level spell with this trait;
you regain the ability to cast it when you finish a long rest. Once
you reach 5th level, you can also cast the darkness spell once per day
with this trait; you regain the ability to cast it when you finish a
long rest. Charisma is your spellcasting ability for these spells.
However, in Mordenkainen's Tome of Foes (MToF, p. 21-23), the "Tiefling Subraces" section outlines optional rules for DMs to allow more variety. The point of these variants is that some of your racial traits (that replace the Ability Score Improvement and Infernal Legacy traits) are linked to one of the Lords of the Nine Hells. The vanilla version in the PHB is based on an infernal connection with Asmodeus; however, there are another 8 options in MToF to choose from.
As you mention, you can create a separate sheet for each of the nine versions – possibly "Tiefling of Asmodeus' Legacy", and so on.
I've included below the cantrip and spells attained at 3rd and 5th level, in that order.
- Asmodeus: thaumaturgy; hellish rebuke; darkness
- Baalzebul: thaumaturgy; ray of sickness; crown of madness
- Dispater: thaumaturgy; disguise self; detect thoughts
- Fierna: friends; charm person; suggestion
- Glasya: minor illusion; disguise self; invisibility
- Levistus: ray of frost; armor of Agathys; darkness
- Mammon: mage hand; Tenser's floating disk; arcane lock
- Mesiphistopheles: mage hand; burning hands; flame blade
- Zariel: thaumaturgy; searing smite; branding smite
Also, keep in mind that the ability score changes depend on the subrace as well. You can find these in the PHB and MToF on the pages I've listed already.
I find that, whenever I've created a homebrew race, I want to keep it in balance so I refer to the other published races.
This is suggested in the DMG section on Creating New Race (p. 286):
When creating a race [...] Compare your creation to the other races of
your world, and borrow freely from the traits of other races.
Though, some have more advantages than others at first sight, it also does depend on your campaign and world setting.
For instance, in a world where there are very few humanoid races with darkvision, a Tiefling with Asmodeus' or Levistus' Infernal Legacy would have a distinct advantage by not only having darkvision (like all Tieflings) but also being able to cast darkness in between long rests.
As a DM, it has been my experience that players have enjoyed being able to choose an option of the Infernal Legacy. There was a campaign, too, where one of the PCs was reincarnated into a Tiefling, in which case we agreed I would randomise the outcome using a d10 and allowing to re-roll if it landed on a 10 (i.e. a "0" on the die).
Also, it will depend on what class your players want to role-play as well. For instance I had a player who wanted to play a Tiefling Rogue. She chose to have a connection to Glasya which provided her with a distinct advantage. Her PC got a +1 to Dexterity and access very versatile spells within the first 5 levels: minor illusion, disguise self, and invisibility. She used them very creatively in the campaign and it was a lot of fun. Not only that, she got +2 to Charisma as well. This, in combination with her putting her expertise on Deception and Persuasion, made her a formidable character. She kept the NPCs on their toes – and me, because I had to be quite adaptive with role-playing and a more flexible story line. It was great.
I feel there is a bigger question at hand about balancing out races, but there are plenty of questions on this topic already on this site.
I'm not sure the need to change the Infernal Legacy too much is necessary. However, if you want to it is important to think of the overall balance of all the racial traits in conjunction, where Tieflings have the standard +2 and +1 to an ability score, but they also have Darkvision and Hellish Resistance (resistance to fire damage).
You mentioned the possibility of flight like the Aarakocra have. Admittedly, this is a major advantage beyond what most playable races would have. However, if you do allow for this to be a Teifling trait I would remove either Darkvision or the fire resistance, to balance it out.
I think tweaking Infernal Legacy might be a better way to go with this. You can create your own homebrewed list of options. The PC gets one cantrip, one 1st-level spell at 3rd level, and one 2nd-level spell upon reaching 5th level. You can give them a list of options to choose from, or you can let them choose. This will depend on your campaign and the role of magic in your world setting. This way you can also be pretty sure that the Tiefling race will be pretty balanced.
I have replaced spells that appear as a racial trait for other spells at times when creating a homebrew version of an existing playable race and this has worked fine, as long as I stick to a spell of the same level.
I hope this is helpful. Happy homebrewing!
Also of interest:
How do I evaluate whether my homebrew race is balanced?