In the present study, we probe the geodesic motion and accretion of particles around the spherically symmetric Dyonic ModMax black hole using isothermal fluid. The geodesic motion of the particles around the black hole leads to the formation of disk like structure during the accretion process. We compute the radiant temperature, radioactive efficiency, radiant flux energy, circular orbits and observe the behavior of particles within stable circular orbits in the equatorial plane. We examine how the particles are perturbed during the process by using restoring forces and the oscillatory behavior of the particles surrounding a compact object and also investigate the fluid’s critical flow and maximum accretion rate. Our findings demonstrate how the black hole parameter $$\gamma $$γ and charge Q affect the circular geodesic of particles as well as the maximum accretion rate of the Dyonic ModMax black hole.