The Josephson effect in a superconductor/triple-quantum-dot ring/superconductor structure is theoretically investigated. We find that in this structure, interdot spin correlation can be driven, which contributes to the occurrence of new 0 and pi phases of the Josephson current. Moreover, in the 0-pi phase-transition process, an intermediate bistable phase appears in which the Josephson current is completely suppressed. By analyzing the interdot spin correlation, the electron motion mechanism is clarified. We then attribute the disappearance of the Josephson current to the occurrence of the Josephson-Fano effect. What is interesting is that the disappearing Josephson current is accompanied by the apparent persistent current in the ring whose direction is determined by the superconducting phase difference. With the calculated results, we consider such a structure to be a candidate for the realization of the persistent current bit.