  We investigate the potential existence of a superconducting phase in $5d$
Mott insulators with an eye to hole doped Sr$_2$IrO$_4$. Using a mean-field
method, a mixed singlet-triplet superconductivity, $d + p$, is observed due to
the antisymmetric exchange originating from a quasi-spin-orbit-coupling. Our
calculation on ribbon geometry shows possible existence of the topologically
protected edge states, because of nodal structure of the superconducting gap.
These edge modes are spin polarized and emerge as zero-energy flat bands,
supporting a symmetry protected Majorana states, verified by evaluation of
winding number and $\mathbb{Z}_2$ topological invariant. At the end, a possible
experimental approach for observation of these edge states and determination of
the superconducting gap symmetry are discussed based on the quasi-particle
interference (QPI) technique.
