Minions are Troll-Related
This is taken from the League of Legends wiki:
"Minions are magical constructs summoned for battles. They are not fully sentient beings, they are controlled by summoners.
Summoning minions requires a constant and massive amount of magical energy. Nexuses focus magical energy from powerful crystals. This energy is enough for sustained minion spawning. The destruction of a nexus stops the summoning magic.
Minion bodies can be magically constructed from several sources, including animated magic scrolls, animated sand, magically animated bolts of cloth, and even sound.
Necromancy is a minion summoning technique that uses dark magic to reanimate Shepherd of Souls.png corpses. Most known practitioners of necromancy come from the Shadow Isles.
While not magically constructed, living minions share many traits with magically constructed minions. Voidborn summoned through Zz'Rot portals are controlled by those who have the magical power required to use them. One of such persons is Malzahar. A Celestial Being known as Bard is frequently followed by minion like spirits known as Meeps that aid him in his tasks (though they are more like companions than outright minions).
The earliest recorded use of minions for battles was at the battlefield known as Summoner's Rift, where summoners from ancient sides known as the Protectorate (Stag crest) and Magelord (Owl crest) fought against each other."
It is not stated that minions have anything to do with trolls anywhere.
Even Jax could be Troll-related
While at first this seemed plausible and I actually believed it for a while given the fact he has three fingers, you never see his face, and in his short story he calls himself a "monster", something that is almost a synonym for a troll (atleast humans think so), however, his feet does not match Trundle's and in his short story he reminisces about Icathia, a lost city located south on the continent of Valoran and he is even affiliated with Ionia on the official League of Legends website for some reason.
Even though Jax's race on the League of Legends wiki is listed as "Unknown (altered by the void)", I don't think he's a troll. Since trolls come from the Freljord, a place located to the north on the continent of Valoran, I doubt they can survive the temperatures of the south or even have a reason to travel down south to begin with.
And as far as I know, trolls don't see themselves as monsters based on one of Trundle's quotes: "I'm not ugly but they are about to be", meaning that trolls/he doesn't find himself/themselves disgusting/repulsing. I think it is more plausible that Jax is a human corrupted by void energies caused by Icathia, transforming him into what he is today. This would also explain why he calls himself a monster in his short story.
I know the League of Legends wiki is neither an official, nor a reliable source of information, but it's the biggest one we have (as far as I know). Correct me if any of the above statements are incorrect.
Link to minions on the League of Legends wiki.
Link to Jax on the League of Legends wiki.
Link to Trundle on the League of Legends wiki.
Link to Jax's short story.