In this study, we examine by comparing the dynamic magnetic and hysteretic properties of Ising-type endohedral fullerene (EF) with various dopant magnetic particles confined within a spherical cage. The model of EF X@C60(Spin-1/2) with X = spin-1/2, spin-1 and spin-3/2 is proposed to study the effect of the nature of core particle on the magnetic properties. The results were obtained by mean-field theory as well as Glauber-type stochastic dynamics, and focused on the response of thermal and hysteretic behaviors of systems. The system exhibits second- and first-order phase transitions. In three different core cases, the system also exhibits type-II superconductivity behavior with a dynamic hysteresis curves of the core. All results display magnetic properties of the EF which strongly depend on the nature of core particle. Moreover, core particle and core/shell (C-S) interaction are proposed as the basic factors affecting the magnetic properties of EF system.