Apatōr means without a father, without record of a father, or fatherless. In Greek culture, the term had legal implications (lacking paternal lineage). In Hebrews 7:3, it is applied to Melchizedek — not that he literally had no father, but that no father is recorded in the Genesis account, making his priesthood appear timeless and eternal.
Hebrews' use of apatōr for Melchizedek is one of the most sophisticated typological arguments in Scripture. Melchizedek's missing genealogy in Genesis prefigures the eternal nature of Christ's priesthood — not inherited, not transient, but permanent. Christ is our High Priest not by biological succession but by the power of an indestructible life (Hebrews 7:16).