We report the observation of sharp suppression of superconductivity-induced zero-bias conductance peaks at low magnetic fields in InSb nanowire Josephson quantum dot devices. With multiple gates, the quantum dot devices can be tuned to the Kondo-superconductivity interplaying regime, in which Kondo-enhanced superconductivity manifests as a zero-bias conductance peak. In weak magnetic fields, the zero-bias conductance peak is found to exhibit an unusual negative magnetoresistance when the Kondo temperature is comparable to the superconductor gap. The observation could not be explained by magnetic field induced 0-$pi$ phase transition, topological phase transition, or other known mechanisms, but may arise from correlation induced interference when Cooper pairs cotunnel through the quantum dots.