We investigate the topological properties and phase diagrams of a one-dimensional Kitaev chain with spin-orbit coupling, subject to an external magnetic field, and hosting coexisting singlet $s$-wave and triplet $p$-wave pairings. To drive the system out of equilibrium, we introduce a phase in the hopping parameter that accounts for a uniform particle current. Using symmetry analysis, we identify the conditions under which the system belongs to the topological class BDI with a $\mathbb{Z}$ invariant. Breaking chiral symmetry by introducing the particle current reduces the classification to topological class D with a ${\mathbb{Z}}_2$ invariant. We calculate the winding number for class BDI and the Pfaffian invariant for class D to obtain the corresponding phase diagrams. In addition, we compute the energy spectrum for class D to determine the phase boundaries analytically, and employ the real-space formulation to numerically obtain the Majorana number maps and verify the analytical results. Our findings highlight how mixed pairing channels and current-induced symmetry breaking enrich the landscape of one-dimensional topological superconductivity and provide new insights into the stability of Majorana modes under nonequilibrium conditions.

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• Majorana zero modes
• Spin-orbit coupling
• Superconductivity
• Topological phases of matter
• Topological superconductors
• 1-dimensional systems
• Bogoliubov-de Gennes equations
• Tight-binding model