  A Sasakian quasi-Killing spinor (SqK-spinor), which is a generalization of a
Killing spinor on Sasakian manifolds, was defined in \cite{Kim Friedrich
2000}.The purpose of this paper is to study in detail SqK-spinors on
three-dimensional pseudo-Riemannian Sasakian space-form.We briefly review some
results on SqK-spinors and then investigate some geometric properties.First, we
demonstrate that the Reeb vector field is described by a specific SqK-spinor.
Then we establish that the motion of a charged particle in the presence of a
contact Maxwell field can be depicted using an SqK-spinor. urthermore, we find
that almost all SqK-spinors provide solutions to the Einstein-Dirac system with
a non-zero cosmological constant.Additionally, we reveal that a particular
SqK-spinor in conjunction with a contact Maxwell field satisfies the
Einstein-Dirac-Maxwell systems.Finally, we show explicit formulae of
SqK-spinors in terms of elementary functions with respect to a certain frame.
