This paper investigates the geodesic motion and circular motion of particles around a linear Maxwell \(f(R)\) black hole in a modified gravity black hole field, using a specific metric. It focusses on framing the effective potential function for photon-like as well as massive particles, revealing differences in the behaviour of coordinate and proper time relative to radial distance in the space–time geometry. The analysis focusses on effective potential curves obtained from specific equations, examining the dynamics of massless and massive particles in different scenarios. Moreover, it examines the stability of particle orbits using the Lyapunov exponent and explains how the circular orbit of a particle moving under the influence of gravitational field of the black hole is conditionally stabilised. This paper examines how the cosmological constant and gravitational modification parameter influence the circular and geodesic motion of the particle. Finally, this paper provides a graphical analysis of the radius of the innermost stable circular orbit and outermost stable circular orbit of the particles moving in the field of modified gravity.
