In this study, effective-field calculations within Ising model framework have been utilised to investigate theoretically the effect of temperature and interaction parameters on the magnetic and hysteretic processes in an idealised system used to represent endohedral fullerene (EF) with a dopant magnetic atom confined within a spherical cage. The thermal behaviour of the partial (centre and surface) and the total magnetizations are studied to determine the character of phase transition (continuous and discontinuous) and to elaborate the phase diagram in interaction parameters plane. The total and partial hysteresis curves with susceptibility peaks and coercive fields are also given and focused on the influence of the temperature and interaction parameters. According to values of Hamiltonian parameters, the system exhibits the first- and second-order phase transitions and three types of compensation behaviour, namely Q-, R-, and S-types. In the phase diagram of the system, when the centre-surface (C-S) interaction increases or decreases, the phase transition temperature increases symmetrically. Finally, from the hysteresis curves of the system, we observed that type II superconducting-like behaviour can appear by the presence of dopant centre magnetic atom.