  We show the presence of Majorana edge modes in an interacting fermionic
ladder with spin in a number conserved setting. The interchain single particle
hopping is suppressed and only a pair hopping is present between the different
chains of the ladder. Additionally, the hopping along the chains is spin
imbalanced and a transverse magnetic field is applied breaking time-reversal
invariance. We study the robustness of the topological phase with respect to an
on-site interaction between the spin-up and spin-down fermions and the spin
dependent imbalance of the hopping. The main result of the present work is that
the topological phase survives for a finite region in the parameter space in
the presence of interactions. The localized Majorana edge modes seems to be
more stable in the case when the on-site interaction is an attraction.
