  The formation of a naked singularity in $f(R)$ global monopole spacetime is
considered in view of quantum mechanics. Quantum test fields obeying the
Klein$-$Gordon, Dirac and Maxwell equations are used to probe the classical
timelike naked singularity developed at $r=0$. We prove that the spatial
derivative operator of the fields fails to be essentially self-adjoint. As a
result, the classical timelike naked singularity formed in $f(R)$ global
monopole spacetime remains quantum mechanically singular when it is probed with
quantum fields having different spin structures. Pitelli and Letelier (Phys.
Rev. D 80, 104035, 2009) had shown that for quantum scalar ($spin$ $0$% )
probes the general relativistic global monopole singularity remains intact. For
specific modes electromagnetic ($spin$ $1$) and Dirac field ($% spin$ $1/2$)
probes, however, we show that the global monopole spacetime behaves quantum
mechanically regular. The admissibility of this singularity is also
incorporated within the Gubser's singularity conjecture.
