  The formation of naked singularities in $2+1-$ dimensional power - law
spacetimes in linear Einstein-Maxwell and Einstein-scalar theories sourced by
azimuthally symmetric electric field and a self-interacting real scalar field
respectively, are considered in view of quantum mechanics. Quantum test fields
obeying the Klein-Gordon and Dirac equations are used to probe the classical
timelike naked singularities developed at $r=0$. We show that when the
classically singular spacetimes probed with scalar waves, the considered
spacetimes remains singular. However, the spinorial wave probe of the
singularity in the metric of a self-interacting real scalar field remains
quantum regular. The notable outcome in this study is that the quantum
regularity/singularity can not be associated with the energy conditions.
