The clear identification of Majorana modes remains one of the most challenging unresolved issues in condensed matter physics. The authors explore the thermoelectric properties transverse to quantum-dot-based Josephson junctions in a novel four-terminal configuration. The superconducting phase dependence introduces a distinctive control mechanism that significantly aids in detecting signatures of Majorana states. This is evidenced by their impact on transverse electrical and thermal conductances, the Seebeck coefficient, and the observed violation of the Wiedemann-Franz law.