[Cicero]

Yes, just so. And the Muslim atrocities during the period leading up to the fall of Byzantium were frequent and horrible, in the lands of Asia Minor.

After the fall of Byzantium, the Turks took over Greece. One of the taxes the Greeks were forced to pay was a certain number of newly born children from each village, who were taken in caravans and by ship to Byzantium where they became slaves of the Turks. Many were trained up as Janissaries--formerly Christian children raised to fight against their own people.

[Verginius Rufus]

The Ottomans' "blood tribute" was of young boys from Christian villages, not newborns, and not only from Greek villages. Ivo Andric's novel The Bridge on the Drina centers around a bridge in Visegrad, Bosnia, which was built on the orders of a Grand Vizier who had been taken from that area as a boy in the blood tribute and later rose to the highest position in the sultan's bureaucracy.