  We obtain a class of magnetically charged solutions in 2+1 dimensional
Einstein - Power - Maxwell theory. In the linear Maxwell limit, such
horizonless solutions are known to exist. We show that in 3D geometry, black
hole solutions with magnetic charge does not exist even if it is sourced by
power-Maxwell field. Physical properties of the solution with particular power
k of the Maxwell field is investigated. The true timelike naked curvature
singularity develops when k>1 which constitutes one of the striking effects of
the power Maxwell field. For specific power parameter k, the occurrence of
timelike naked singularity is analysed in quantum mechanical point of view.
Quantum test fields obeying the Klein - Gordon and the Dirac equations are used
to probe the singularity. It is shown that the class of static pure magnetic
spacetime in the power Maxwell theory is quantum mechanically singular when it
is probed with fields obeying Klein-Gordon and Dirac equations in the generic
case.
