  The transport behavior of a double quantum dot side-attached to a topological
superconducting wire hosting Majorana zero-energy modes is studied
theoretically in the strong correlation regime. It is shown that Majorana modes
can leak to the whole nanostructure, giving rise to a subtle interplay between
the two-stage Kondo screening and the half-fermionic nature of Majorana
quasiparticles. In particular, the coupling to the topological wire is found to
reduce the effective exchange interaction between the two quantum dots in the
absence of normal leads. Interestingly, it also results in an enhancement of
the second-stage Kondo temperature when the normal leads are attached.
Moreover, it is shown that the second stage of the Kondo effect can become
significantly modified in one of the spin channels due to the interference with
the Majorana zero-energy mode, yielding the low-temperature conductance equal
to $G=G_0/4$, where $G_0 = 2e^2/h$, instead of $G=0$ in the absence of the
topological superconducting wire. We also identify a nontrivial spin-charge
${\rm SU}(2)$ symmetry present in the system at a particular point in parameter
space, despite lack of the spin nor charge conservation. Finally, we discuss
the consequences of a finite overlap between two Majorana modes, as relevant
for short Majorana wires.
