Twin-Peak Quasi-Periodic Oscillations and Orbital Dynamics in Einstein–Nonlinear Maxwell–Yukawa Spacetime

In this work, we study the orbital dynamics of a test particle and the characteristics of twin-peak quasi-periodic oscillations (QPO) in Einstein–Nonlinear Maxwell–Yukawa (ENLMY) spacetime. The influence of the Yukawa screening parameter [Formula: see text] and black hole charge [Formula: see text] on the horizon structure, specific energy [Formula: see text] and specific angular momentum [Formula: see text] of circular orbits, as well as on characteristic orbital radii such as [Formula: see text], [Formula: see text], and [Formula: see text], was consistently investigated. The charge parameter lowers the minima of [Formula: see text] and [Formula: see text] and shifts them toward the black hole, whereas the Yukawa screening redistributes the preferred circular-orbit region toward larger radii. Our results demonstrate that an increase in charge [Formula: see text] shifts all circular-orbit boundaries inward, leading to a monotonic decrease in [Formula: see text], [Formula: see text], and [Formula: see text]. Conversely, an increase in the Yukawa parameter [Formula: see text] pushes these radii outward. This indicates that electromagnetic deformation and screening effects influence the spacetime geometry in opposite directions. A comparison of the ER2, ER3, and ER4 QPO models revealed that parameter sensitivity in ENLMY spacetime is model-dependent. While an increase in charge leads to an increase in the upper frequency [Formula: see text], the parameter [Formula: see text] significantly alters the frequency-radius correspondence. Due to the presence of [Formula: see text] parameters, the same [Formula: see text] pair can correspond to different parameter combinations, which creates an additional source of degeneracy in parameter estimation based on QPO observations. We also constrained the ENLMY parameters for H 1743–322 and M82 X–1 through MCMC analysis, obtaining mass estimates compatible with their stellar-mass and intermediate-mass black-hole interpretations, respectively.