  Quantum singularities considered in the 3D BTZ spacetime by Pitelli and
Letelier (Phys. Rev. D77: 124030, 2008) is extended to charged BTZ and 3D
Einstein-Maxwell-dilaton gravity spacetimes. The occurence of naked
singularities in the Einstein-Maxwell extension of the BTZ spacetime both in
linear and non-linear electrodynamics as well as in the
Einstein-Maxwell-dilaton gravity spacetimes are analysed with the quantum test
fields obeying the Klein-Gordon and Dirac equations. We show that with the
inclusion of the matter fields; the conical geometry near r=0 is removed and
restricted classes of solutions are admitted for the Klein-Gordon and Dirac
equations. Hence, the classical central singularity at r=0 turns out to be
quantum mechanically singular for quantum particles obeying Klein-Gordon
equation but nonsingular for fermions obeying Dirac equation. Explicit
calculations reveal that the occurrence of the timelike naked singularities in
the considered spacetimes do not violate the cosmic censorship hypothesis as
far as the Dirac fields are concerned. The role of horizons that clothes the
singularity in the black hole cases is replaced by repulsive potential barrier
against the propagation of Dirac fields.
