  We investigate the unusual properties of quasirelativistic massless fermions
under a magnetic or electric field by means of nonminimal couplings. Within
this approach, the spin-orbit coupling (SOC) effects are properly generated in
the energy spectrum of the quasiparticles. By including a magnetic field, $B$,
we show that the spin splitting of Landau Levels (LL) obeys a $\sqrt{B}$ linear
dependence with SOC, typical of relativistic particles. Moreover, our
calculated spectrum of LLs resembles the behavior of the three-dimensional (3D)
massless Kane fermions. Using a nonminimal coupling with an external electric
field, we demonstrate that a Rashba-like SOC naturally appears into the
relativistic equations and apply to the case of two-dimensional (2D) massless
Dirac fermions. Still considering our proposed approach, the Hall conductivity
is also computed for the 2D case under transverse electric field both at zero
and finite temperatures for a general chemical potential. The results feature a
typical quantization of the Hall conductivity at low temperatures, when the
absolute value of the gap opened by the electric field is larger than the
considered chemical potential.
