In this story magic is a real thing, but it's rare, and random. Children will spring up -- not all the time, but occasionally -- with strong magical abilities.

Sometimes, if remote enough, these people will be shamans or scions or something to their town or villiage. Anywhere closer to the major centres, though, and someone with power will take notice. Most typically, that will involve an established magical warlord in the area showing up to snuff out the child, in order to retain control over the population.

Occasionally someone will go undetected and go off into the wilds to study in peace, sometimes they'll learn to control their magic just enough to blend in. Occasionally someone stands up to challenge the current warlord and there's a change in power.

Other potential ideas

This is all going on in the middle areas, that are populated but not strongly so. In the next province over, they embrace magic. Mages are a trade, and they have a guild, and apprentice, and all that stuff.

Someone in the area who has strong magic, but was remote enough to escape notice, wants to try and start a guild (if that last idea is off the ground, it's possible they're instead someone from that province coming over). So, they go around to the children that would normally be killed by the warlords, but he gets there first and takes the kid.