A Zeeman-insensitive optical clock atomic transition is engineered when nuclear spins are dressed by a nonresonant radio-frequency field. For fermionic species as Sr87, Yb171, and Hg199, particular ratios between the radio-frequency driving amplitude and frequency lead to “magic” magnetic values where a net cancelation of the Zeeman clock shift and a complete reduction of first-order magnetic variations are produced within a relative uncertainty below the 10−18 level. An Autler-Townes continued fraction describing a semiclassical radio-frequency dressed spin is numerically computed and compared to an analytical quantum description including higher-order magnetic field corrections to the dressed energies.