I didn't know an Abyssal tiefling is already incorporated into the game. If so, yay! It should definitely be fully on par with Asmodeus tiefling.
It should also have some nice backstory we could adhere to, such as "they were a warrior in Blood Wars" or "they were summoned from the Abyss and then broke the spell that had bound them".
Unfortunately the Abyssal UA (Unearthed Arcana - Official Playtest Material), was never implemented and is pretty much assumed to be dead (the UA was released in 2015). Pity as it was
fairly interesting (it gave you a semi-random cantrip and spell(s) after each long rest).
Personally I always wanted to play as a
Yugoloth Tiefling (The Neutral Evil equivalent to Demon's Chaotic Evil and Devil's Lawful Evil), basically you're a Demonic Mercenary up for anything so long as the gold is right.