Observational constraints on f(R, T) gravity coupled with NED from black hole quasi periodic oscillations

In this work, we examine the influence of nonlinear electrodynamics (NED) and f ( R, T ) gravity on quasi-periodic oscillations (QPOs) around a magnetically charged black hole. By analyzing the effective potential, specific energy, and angular momentum of circular orbits, we study how the NED parameter α and the gravitational coupling parameter β affect orbital dynamics. Increasing α leads to systematic deviations from the Reissner-Nordström behavior, reflected in shifts in the ISCO radius and orbital frequencies. We further explore QPO-generating radii using the Relativistic Precession (RP), Warped Disk (WD), and Epicyclic Resonance (ER2-ER4) models. We further extend our analysis by performing an MCMC-based parameter estimation using QPO data from black holes spanning a wide range of mass scales. This approach yields consistent observational constraints on the model parameters.