We introduce the α-κ-μ shadowed (α-KMS) fading distribution as a natural generalization of the versatile α-κ-μ and α-η-μ distributions. The α-KMS fading distribution unifies a wide set of fading distributions, as it includes the α-κ-μ, α- η-μ, α-μ, Weibull, κ-μ shadowed, Rician shadowed, κ-μ and η- μ distributions as special cases, together with classical models like Rice, Nakagami-m, Hoyt, Rayleigh and one-sided Gaussian. Notably, the α-KMS distribution reduces to a finite mixture of α-μ distributions when the fading parameters μ and m take positive integer values, so that performance analysis over α-KMS fading channels can be tackled by leveraging previous (existing) results in the literature for the simpler α-μ case. As application examples, important performance metrics like the outage probability and average channel capacity are analyzed.