  The Event Horizon Telescope (EHT) imaging of the supermassive black holes at
the centers of Messier 87 galaxy and the Milky Way galaxy marks a significant
step in observing the photon rings and central brightness depression that
define the optical appearance of black holes with an accretion disk scenario.
Inspired by this, we take into account a static and spherically symmetric
magnetically charged regular black hole (MCRBH) metric characterized by its
mass and an additional parameter q, which arises from the coupling of Einstein
gravity and nonlinear electrodynamics (NLED) in the weak field approximation.
This parameterized model offers a robust foundation for testing the coupling of
Einstein gravity and NLED in the weak-field approximation, using the EHT
observational results. In this study, we investigate the geodesic motion of
particles around the solution, followed by a discussion of its fundamental
geometrical characteristics such as scalar invariants. Using null geodesics, we
examine how the model parameter influences the behavior of the photon sphere
radius and the associated shadow silhouette. We seek constraints on q by
applying the EHT results for supermassive black holes M87* and Sgr A*.
Furthermore, it is observed that the geodesics of time-like particles are
susceptible to variations in q, which can have an impact on the traits of the
innermost stable circular orbit and the marginally bounded orbit. Our primary
objective is to probe how the free parameter q affects various aspects of the
accretion disk surrounding the MCRBH using the thin-disk approximation. Next,
we discuss the physical characteristics of the thin accretion disk as well as
the observed shadows and rings of the MCRBH, along with its luminosity, across
various accretion models. Ultimately, variations in accretion models and the
parameter q yield distinct shadow images and optical appearances of the MCRBH.
