Topological Ising superconductivity in two-dimensional p-wave magnet

Fermi-surface spin splitting generated by non-relativistic exchange fields provides a new route to topological superconductivity without relying on strong spin-orbit coupling. Here, we study superconducting instabilities of a square-lattice $p$-wave magnet with onsite and nearest-neighbour attractive interactions. The odd-parity exchange field removes inversion symmetry in the spin-split electronic structure, allowing singlet and triplet order parameters to mix within a single $A_1$ symmetry channel. The leading instability is a coupled $s+p_x$ Ising state, whose singlet-triplet balance is continuously tunable by the relative strength of the nearest-neighbour attraction. When the triplet gap amplitude exceeds the singlet one, this Ising state undergoes a transition into a nodal topological superconducting phase with Majorana edge modes protected by momentum-resolved winding numbers. These modes extend over finite momentum intervals bounded by the surface projections of bulk point nodes. We further show that a Zeeman field perpendicular to the exchange field can induce a $Z_2$ topological superconducting phase, even in the regime where a single gap dominates.