This paper investigates the orientation-dependent Josephson effect in spin-singlet superconductor/alternagnet/spin-triplet superconductor (SS/AM/TS) junctions. Using the Green's function method, the study reveals that the current-phase difference relationships (CPRs) in these junctions strongly depend on the orientation of the alternagnet and the types of Cooper pairs. For orientations at odd multiples of π/4, the CPRs are of the sin2φ type, independent of the pairing wave functions. For other orientations, the lowest order current emerges, with its form (sinφ or cosφ) depending on the pairing wave functions. The φ₀ phase and 0-π transition can be realized in these junctions. The selection rules for the lowest order current are presented, and symmetric relations of the CPRs are analyzed under mirror reflection, time-reversal, and spin rotation operations. The results provide a method to detect intrinsic spin-triplet superconductivity and have applications in designing field-free quantum devices. The study also highlights the unique transport properties and the novel interplay between alternagnetism and spin-triplet superconductivity in SS/AM/TS junctions.This paper investigates the orientation-dependent Josephson effect in spin-singlet superconductor/alternagnet/spin-triplet superconductor (SS/AM/TS) junctions. Using the Green's function method, the study reveals that the current-phase difference relationships (CPRs) in these junctions strongly depend on the orientation of the alternagnet and the types of Cooper pairs. For orientations at odd multiples of π/4, the CPRs are of the sin2φ type, independent of the pairing wave functions. For other orientations, the lowest order current emerges, with its form (sinφ or cosφ) depending on the pairing wave functions. The φ₀ phase and 0-π transition can be realized in these junctions. The selection rules for the lowest order current are presented, and symmetric relations of the CPRs are analyzed under mirror reflection, time-reversal, and spin rotation operations. The results provide a method to detect intrinsic spin-triplet superconductivity and have applications in designing field-free quantum devices. The study also highlights the unique transport properties and the novel interplay between alternagnetism and spin-triplet superconductivity in SS/AM/TS junctions.