<p>We examine the interplay between the Nagaoka ferromagnetism and superconducting pairing correlations in a two-by-two quantum dot array proximitized by an <i>s</i>-wave superconductor. Focusing on the subgap regime, we determine the phase diagram of the system, demonstrating that Nagaoka ferromagnetism becomes greatly affected by the presence of superconductor and, depending on the strength of direct and crossed Andreev reflections, can be fully suppressed. This happens at some critical value of the induced on-dot pairing potential, for which we provide the corresponding analytical formulas in the limit of large Coulomb correlations. Moreover, we also shed light on the competition between Nagaoka ferromagnetism and superconductivity visible in the transport characteristics. Using the real-time diagrammatic technique, we determine the nonequilibrium current and differential conductance assuming that the quantum dot plaquette is weakly coupled to external lead that can be used to probe the system’s properties. We not only uncover the impact of Nagaoka ferromagnetism on the Andreev current and differential conductance, but also demonstrate a spin quintuplet blockade of the Andreev transport.</p>