The author presents a detailed analysis of the spinor version of the Kähler equation. The tensor version of this equation was introduced by \textit{E. Kähler} [Rend. Mat. Appl., V. Ser. 21, 425-523 (1963; Zbl 0127.314)], and involves an inhomogeneous differential form which is naturally associated with a Clifford algebra. It may be of importance in the theory of fermion fields in a quantum gravity context. A class of solutions of Kähler spinors is constructed which -- in a perturbation-theoretic approach -- decouple the Kähler equation. It is shown how the propagation of \(\beta\)-Kähler spinors is influenced by an interaction term in a space-time of constant curvature. Contents include: an introduction, Riemannian normal coordinates, the Kähler equation, and \(\beta\)-spinors in Riemannian normal coordinates.