  Recently, the anomalous decay rate of quasinormal modes has been studied for
some geometries under scalar field perturbations, which occurs when the
longest-lived modes are the ones with higher angular number, as well as, the
existence of a critical scalar field mass, i.e the value of scalar field mass
such that the decay rate does not depend appreciably on the angular number, and
beyond which the behaviour of the decay rate is inverted. Here, we consider the
propagation of fermionic fields in the background of Schwarzschild de Sitter
black holes, and we show that the anomalous decay rate behaviour and the fine
structure, related to the coupling between the chirality and the mass of the
field, can be observed in the fermionic spectrum.
