  Both the collider searches and direct detections are promising approaches to
probe a fermionic dark matter. In this paper we study signatures of the four
fermion contact operators involving a dark fermion, an electron and a quark
pair. We show that the mono-electron production channel at hadron collider can
provide strong constraints. Associated productions of a charged electron with a
photon/jet with missing energy are also studied. Using the current LHC data at
$\sqrt{s} = 13$\,TeV, the lower bound on the energy scale of the (axial-)vector
operator can reach to $12$\,TeV for a massless dark fermion. It can be further
improved to about $24$\,TeV at the HE-LHC with $\sqrt{s} = 25$\,TeV and a total
luminosity $20\,{\rm ab}^{-1}$. For the direct detections, the signal operators
can generate induced $\beta^\pm$ decays. For the induced $\beta^-$ decay, we
show that the constraints are weaker than the ones from the collider searches
in almost all of the parameter space, and the accessible parameter space is
already excluded by the current LHC data. In case of a relative heavy dark
fermion (a few MeV), the induced $\beta^+$ decay is more sensitive than the
collider search. Despite the advantage of the collider search that a much wider
range of the dark fermion mass can be investigated, it can also provide a
complementarity to the detect detections.
