This study investigates the quantum Mpemba effect (QMPE) in nonequilibrium open quantum systems, focusing on quantum dot and two-site fermionic systems coupled to two baths. The Mpemba effect, originally observed in classical systems where hotter water freezes faster than colder water, has been generalized to quantum systems, where it manifests as anomalous relaxation or inverse relaxation dynamics. In this work, the researchers explore how nonequilibrium conditions, where the system does not approach an asymptotic equilibrium state but instead remains in a steady state sustained by continuous energy injection from baths, can enhance the emergence of the Mpemba effect. The study shows that nonequilibrium conditions significantly expand the parameter space where the Mpemba effect occurs. This is demonstrated through the analysis of quantum correlations, such as entanglement and quantum mutual information (QMI), in both quantum dot and two-site fermionic systems. The results indicate that the nonequilibrium environment can either accelerate or delay the Mpemba effect, depending on the system's initial conditions and bath parameters. Additionally, the study highlights the role of quantum coherence in the emergence of the Mpemba effect, showing that quantum coherence can significantly influence the dynamics of the system, leading to the observation of the QMPE even when conventional Lindbladian dynamics predict otherwise. The research also reveals that the Mpemba effect can occur in systems with multiple baths, where the nonequilibrium conditions allow for a broader range of parameter regimes to support the effect. The study provides a detailed analysis of the dynamics of quantum correlations, showing that the Mpemba effect can manifest as crossings in the evolution of entanglement and QMI. These findings suggest that the Mpemba effect is not limited to classical systems but can also occur in quantum systems under nonequilibrium conditions, opening new avenues for experimental investigation. The results demonstrate that the Mpemba effect is a robust phenomenon in nonequilibrium quantum systems, with quantum coherence playing a crucial role in its emergence.This study investigates the quantum Mpemba effect (QMPE) in nonequilibrium open quantum systems, focusing on quantum dot and two-site fermionic systems coupled to two baths. The Mpemba effect, originally observed in classical systems where hotter water freezes faster than colder water, has been generalized to quantum systems, where it manifests as anomalous relaxation or inverse relaxation dynamics. In this work, the researchers explore how nonequilibrium conditions, where the system does not approach an asymptotic equilibrium state but instead remains in a steady state sustained by continuous energy injection from baths, can enhance the emergence of the Mpemba effect. The study shows that nonequilibrium conditions significantly expand the parameter space where the Mpemba effect occurs. This is demonstrated through the analysis of quantum correlations, such as entanglement and quantum mutual information (QMI), in both quantum dot and two-site fermionic systems. The results indicate that the nonequilibrium environment can either accelerate or delay the Mpemba effect, depending on the system's initial conditions and bath parameters. Additionally, the study highlights the role of quantum coherence in the emergence of the Mpemba effect, showing that quantum coherence can significantly influence the dynamics of the system, leading to the observation of the QMPE even when conventional Lindbladian dynamics predict otherwise. The research also reveals that the Mpemba effect can occur in systems with multiple baths, where the nonequilibrium conditions allow for a broader range of parameter regimes to support the effect. The study provides a detailed analysis of the dynamics of quantum correlations, showing that the Mpemba effect can manifest as crossings in the evolution of entanglement and QMI. These findings suggest that the Mpemba effect is not limited to classical systems but can also occur in quantum systems under nonequilibrium conditions, opening new avenues for experimental investigation. The results demonstrate that the Mpemba effect is a robust phenomenon in nonequilibrium quantum systems, with quantum coherence playing a crucial role in its emergence.