This study investigates the emergence of pair density wave (PDW) states and the supercurrent diode effect in metallic altern magnets (AMs) with momentum-dependent spin splitting. The research focuses on BCS-type attractive interactions and finds that symmetrically distinct PDW states, including Fulde-Ferrell (FF) and Fulde-Ferrell * (FF*) states, can be stabilized depending on the chemical potential. These states break inversion symmetry and exhibit non-reciprocal supercurrents. The supercurrent diode effect is proposed as a tool to distinguish between different PDW states in AMs. The study also explores the relation between PDW states and material candidates such as RuO₂ thin films and hole-doped La₂CuO₄. The research derives the Ginzburg-Landau theory from a microscopic model and shows that non-reciprocal supercurrents can appear for intrinsic inversion-symmetry breaking bulk superconducting states of AMs. The phase diagram of superconducting states in the weak-coupling limit is obtained by minimizing the Ginzburg-Landau free energy. The PDW order parameter is written as {Δ_q, Δ_{\bar{q}}, Δ_{-q}, Δ_{-\bar{q}}}, with corresponding wavevectors {q, \bar{q}, -q, -\bar{q}}. The free energy is constructed by imposing gauge, translational, inversion, and magnetic fourfold rotational symmetries. The study finds that the system stabilizes the FF state when μ/c₀ < 0.18 and the FF* state when 0.18 ≤ μ/c₀ < 0.23. The FF* state can induce non-reciprocal supercurrents in both the x and y directions, unlike the FF state which induces non-reciprocal current only in the x direction. The supercurrent diode effect is quantified by a diode coefficient η, which is defined as (J_c^+ - J_c^-)/(J_c^+ + J_c^-). The coefficient η reaches its maximum value of 0.5 at μ/c₀ = 0.17 near the phase boundary between the FF and FF* states. The study also explores the potential of PDW formation with different pairing symmetries and topological properties, such as spin-triplet pairing or in the presence of Rashba spin-orbit coupling. The research highlights the potential of materials like RuO₂ thin films and hole-doped La₂CuO₄ for studying the interplay between alternagnetism and superconductivity. The study concludes that the supercurrent diode effect can be utilized to detect different types of PDW states in future experiments.This study investigates the emergence of pair density wave (PDW) states and the supercurrent diode effect in metallic altern magnets (AMs) with momentum-dependent spin splitting. The research focuses on BCS-type attractive interactions and finds that symmetrically distinct PDW states, including Fulde-Ferrell (FF) and Fulde-Ferrell * (FF*) states, can be stabilized depending on the chemical potential. These states break inversion symmetry and exhibit non-reciprocal supercurrents. The supercurrent diode effect is proposed as a tool to distinguish between different PDW states in AMs. The study also explores the relation between PDW states and material candidates such as RuO₂ thin films and hole-doped La₂CuO₄. The research derives the Ginzburg-Landau theory from a microscopic model and shows that non-reciprocal supercurrents can appear for intrinsic inversion-symmetry breaking bulk superconducting states of AMs. The phase diagram of superconducting states in the weak-coupling limit is obtained by minimizing the Ginzburg-Landau free energy. The PDW order parameter is written as {Δ_q, Δ_{\bar{q}}, Δ_{-q}, Δ_{-\bar{q}}}, with corresponding wavevectors {q, \bar{q}, -q, -\bar{q}}. The free energy is constructed by imposing gauge, translational, inversion, and magnetic fourfold rotational symmetries. The study finds that the system stabilizes the FF state when μ/c₀ < 0.18 and the FF* state when 0.18 ≤ μ/c₀ < 0.23. The FF* state can induce non-reciprocal supercurrents in both the x and y directions, unlike the FF state which induces non-reciprocal current only in the x direction. The supercurrent diode effect is quantified by a diode coefficient η, which is defined as (J_c^+ - J_c^-)/(J_c^+ + J_c^-). The coefficient η reaches its maximum value of 0.5 at μ/c₀ = 0.17 near the phase boundary between the FF and FF* states. The study also explores the potential of PDW formation with different pairing symmetries and topological properties, such as spin-triplet pairing or in the presence of Rashba spin-orbit coupling. The research highlights the potential of materials like RuO₂ thin films and hole-doped La₂CuO₄ for studying the interplay between alternagnetism and superconductivity. The study concludes that the supercurrent diode effect can be utilized to detect different types of PDW states in future experiments.