  We have recently shown [Phys. Rev. B {\bf 89}, 165314 (2014)] that a
non--interacting quantum dot coupled to a one--dimensional topological
superconductor and to normal leads can sustain a Majorana mode even when the
dot is expected to be empty, \emph{i.e.}, when the dot energy level is far
above the Fermi level of he leads. This is due to the Majorana bound state of
the wire leaking into the quantum dot. Here we extend this previous work by
investigating the low--temperature quantum transport through an {\it
interacting} quantum dot connected to source and drain leads and side--coupled
to a topological wire. We explore the signatures of a Majorana zero--mode
leaking into the quantum dot for a wide range of dot parameters, using a
recursive Green's function approach. We then study the Kondo regime using
numerical renormalization group calculations. We observe the interplay between
the Majorana mode and the Kondo effect for different dot-wire coupling
strengths, gate voltages and Zeeman fields. Our results show that a "0.5"
conductance signature appears in the dot despite the interplay between the
leaked Majorana mode and the Kondo effect. This robust feature persists for a
wide range of dot parameters, even when the Kondo correlations are suppressed
by Zeeman fields and/or gate voltages. The Kondo effect, on the other hand, is
suppressed by both Zeeman fields and gate voltages. We show that the zero--bias
conductance as a function of the magnetic field follows a well--known
universality curve. This can be measured experimentally, and we propose that
the universal conductance drop followed by a persistent conductance of
$0.5\,e^2/h$ is evidence of the presence of Majorana--Kondo physics. These
results confirm that this "0.5" Majorana signature in the dot remains even in
the presence of the Kondo effect.
