We investigate self-consistent unconventional superconductivity in a two-dimensional $d$-wave altermagnetic metal. We find that momentum-dependent altermagnetic spin splitting suppresses opposite-spin-singlet pairing and stabilizes highly anisotropic equal-spin triplet order. In the spin-conserving limit, this directional triplet pairing gives rise to nearly dispersionless Majorana boundary states associated with effective one-dimensional topological channels. Rashba spin-orbit coupling mixes spin sectors, activates additional pairing components, and drives the system into a mixed-parity superconducting state with dispersive Majorana boundary states. The spin-resolved boundary spectra further reveal a characteristic locking between boundary orientation and spin polarization, reflecting the underlying altermagnetic symmetry. These results identify altermagnetic spin splitting as an intrinsic mechanism for selecting unconventional pairing and generating spin-resolved Majorana boundary states without external magnetic fields.

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• Altermagnetism
• Spin-triplet pairing
• Superconducting order parameter
• Topological superconductors
• Altermagnets
• Bogoliubov-de Gennes equations