Which Ottoman institution took Christian boys as a levy and made them the elite corps?

The devshirme - a periodic levy of boys, mostly from Balkan Christian villages, who were taken from their families, converted, educated and placed in the sultan's service. The best went into the palace administration; the rest became Janissaries, the standing infantry.

It is genuinely difficult to categorise. It was a forced conversion and a form of enslavement, and families are recorded hiding or maiming sons to avoid it - and it was also the only route to real power in the empire, since the born Muslim aristocracy was excluded from these posts by design. Grand viziers came out of it, and some families are recorded bribing officials to get a son taken.

The logic was to build a state apparatus with no dynasties in it: men with no local kin, no inherited land, and no loyalty except to the sultan who had made them. It stopped working when the Janissaries began marrying, enrolling their own sons and behaving like the hereditary interest they were built to replace - after which they deposed sultans, resisted every reform, and were destroyed by artillery in their own barracks in 1826.