  We discuss the emergence of zero-energy Majorana modes in a disordered
finite-length p-wave one-dimensional superconducting ring, pierced by a
magnetic flux $\Phi$ tuned at an appropriate value $\Phi=\Phi_*$. In the
absence of fermion parity conservation, we evidence the emergence of the
Majorana modes by looking at the discontinuities in the persistent current
$I[\Phi]$ at $\Phi=\Phi_*$. By monitoring the discontinuities in $I[\Phi]$, we
map out the region in parameter space characterized by the emergence of
Majorana modes in the disordered ring.
