We investigate the Josephson effect of pseudospin-1 fermions in a superconductor/normal/superconductor (S/N/S) junction based on the dice lattice, where the supercurrent is mediated by topological edge states. Two types of staggered magnetizations are applied in the middle N region, respectively. It is shown that, for the A-B-C lattice staggered magnetization, the $0-\pi$ state transition can be realized by modulating the magnetization strength $M$. However, a larger $M$ may inhibit the occurrence of the $0-\pi$ state transition and even the supercurrent. For the A-C lattice staggered magnetization, the oppositely flowing critical supercurrents are asymmetric, indicating a Josephson diode effect (JDE), which is due to spin-resolved edge states possessing different Fermi velocities in opposite directions. In particular, the JDE efficiency can increase from zero to approximately $24\%$ by modulating $M$, giving rise to a high nonreciprocity. Our results not only uncover the unique supercurrent features of pseudospin-1 fermions in the topological dice lattice but also provide an alternative approach for generating the $0-\pi$ state transition and an efficient JDE.

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• Critical current
• Edge states
• Flat bands
• Josephson effect
• Spin-orbit coupling
• Superconductivity
• Josephson junctions
• Topological materials