We study the possibility of obtaining Majorana zero modes (MZMs) in penta-silicene nanoribbons (p-SiNRs). The spinless and full spin p-SiNRs with p-wave superconducting pairing reveal
the emergence of topologically protected MZMs at opposite ends of the p-SiNRs. In our theoretical
description, particularly for the full spin situation, we consider an external magnetic field perpendicularly applied to the nanoribbon plane and an extrinsic Rashba spin-orbit coupling (RSOC),
besides the first nearest neighbor hopping term and p-wave superconducting pairing. The dispersion
relation profiles show the closing and reopening of the superconducting gap for only one spin component, suggesting a spin-polarized topological phase transition (TPT). Associated with these TPTs,
the energy spectrum as a function of the p-SiNRs chemical potential exhibits zero-energy states
and preferential spin direction. It is associated with nonoverlapping wave functions well-localized
at opposite ends of the superconducting p-SiNRs. Our findings strongly suggest the emergence of
topologically protected and spin-polarized MZMs at the p-SiNRs ends.