The Event Horizon Telescope (EHT) imaging of the supermassive black holes at the centers
of Messier 87 galaxy (M87) and the Milky Way galaxy (Sgr A) 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.