  Zero energy modes are shown to exist in silicene under suitably chosen
magnetic as well as electric fields. Two Majorana modes are found on the
application of opposite local magnetization on the silicene sub-lattices. We
identify a non-Majorana zero energy mode carrying pure spin current under the
influence of inhomogeneous gate electric field. In both cases, wave functions
reveal subtle interference pattern in phase space, showing structures finer
than the Planck constant $\hbar$. A spin system coupled through spin-spin
($\sigma_{z}\otimes\sigma_{z}$) interaction with the Majorana modes exhibits
periodic revival of coherence with a minimum period $\sim $1/n. The same system
shows decoherence-free evolution in the case of gate electric field. Under a
momentum dependent interaction, one Majorana mode having a bound state in the
continuum character is found to be more robust as compared to the other. The
mode arising on application of electric field shows rapid loss of coherence for
such an interaction.
