  In light of the significance of non-commutative quaternionic algebra in
modern physics, the current study proposes the existence of the Klein paradox
in the quaternionic (3+1)-dimensional space-time structure. By introducing the
quaternionic wave function, we rewrite the Klein-Gordon equation in an extended
quaternionic form that includes scalar and vector fields. Because quaternionic
fields are non-commutative, the quaternionic Klein-Gordon equation provides
three separate sets of the probability density and probability current density
of relativistic particles. We explore the significance of these probability
densities by determining the reflection and transmission coefficients for the
quaternionic relativistic step potential. Furthermore, we also discuss the
quaternionic version of the oscillatory, tunnelling, and Klein zones for the
quaternionic step potential. The Klein paradox occurs only in the Klein zone
when the impacted particle's kinetic energy is less than
\mathbb{V}_{0}-m_{0}c^{2}. Therefore, it is emphasized that for the
quaternionic Klein paradox, the quaternionic reflection coefficient becomes
exclusively higher than value one while the quaternionic transmission
coefficient becomes lower than zero.
