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The research of superradiant instability in the realm of quantum gravity is awell-known topic, with many physicists and astronomers studying the potentialimpact it can have on gravitational waves, the structure of the universe, andspacetime itself. In this work, we investigate the superradiant (in)stabilityof a rotating black hole obtained from the nonlinear Maxwell $f(R)$ gravitytheory. In this study, the evaluation of stability/instability is going to bebased on non-existence and existence of magnetic field, when the magnetic fieldconstant becomes $c_{4}=0$ and $c_{4}\neq 0$, respectively. The analyzes ofgreybody factor (GF) and quasinormal modes (QNMs) are investigated in thestationary black hole spacetime both in the absence and presence of themagnetic field parameter. To this end, we first consider the Klein-Gordonequation for the complex scalar field in the geometry of that rotating blackhole. In the sequel, the obtained radial equation is reduced to aone-dimensional Schr\"{o}dinger-like wave equation with an effective potentialenergy. The effects of the nonlinear Maxwell $f(R)$ gravity theory parameters($q$, $c$, and $c_{4}$) on the effective potential, GFs, and QNMs arethoroughly investigated. The obtained results show that even though the factors$q$, $c$, and $c_{4}$ all affect the effective potential, this phenomena,surprisingly, is not valid for the GFs and QNMs. With the proper graphics andtables, all outputs are depicted, tabulated, and interpreted.

Superradiant (In)stability, Greybody Radiation, and Quasinormal Modes of Rotating Black Holes in non-linear Maxwell f (R) Gravity