We investigate the supercurrent flowing in a spin-triplet superconductor (TS) junction with an unconventional $p$-wave magnet (UPM) sandwiched between TS electrodes. It is demonstrated that the UPM functions as a normal metal and supercurrents are hardly affected when the magnetization is aligned with the $\mathbf{d}$ vectors of the TS. In contrast, the supercurrent can be drastically modulated when they are misaligned. A spin supercurrent can be induced due to the $\mathbf{d}$ vector rotated by the UPM and the charge supercurrent can exhibit an abrupt current-reversal effect when the UPM strength vector $\mathit{\alpha }$ is along the longitudinal current direction. The slight deviation of $\mathit{\alpha }$ from the current direction leads to rapid suppression of supercurrents, which is attributed to the different-period oscillation of the momentum-resolved supercurrent induced by the UPM.

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• Spin-triplet pairing
• Altermagnets
• Josephson junctions
• Bogoliubov-de Gennes equations