Controlling magnetic coupling at superconductor-magnet interfaces is a fundamental challenge. Using numerical renormalization group calculations on a strongly correlated molecular dimer coupled to two superconducting electrodes, we report a two-stage quantum phase transition driven solely by the superconducting gap $\mathrm{\Delta }$. As $\mathrm{\Delta }$ increases, the system first transits at ${\mathrm{\Delta }}_{c1}$ from an underscreened Kondo-dominant state to a superconducting-dominant one. Simultaneously, the interorbital exchange mediator shifts from metallic itinerant electrons to virtual single-particle excitations within the gap-a renormalized Ruderman-Kittel-Kasuya-Yosida interaction that sustains ferromagnetic order. Remarkably, at a second critical point ${\mathrm{\Delta }}_{c2}$, the mediator then undergoes a fundamental switch to virtual Cooper pairs from the condensate, triggering an abrupt reversal of the spin correlation from ferromagnetic to antiferromagnetic. This sequential exchange mediator switching, distinct from the conventional picture of a smoothly enhanced Yu-Shiba-Rusinov exchange, establishes a paradigm for actively tuning quantum magnetic states in superconducting heterostructures.

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• Kondo effect
• Magnetic coupling
• Proximity effect
• Quantum phase transitions
• Heavy-fermion systems
• Molecular junctions
• Anderson impurity model