The thermostatistic properties of a q-generalized Fermi system trapped in a generic power-law potential are studied,based on the generalized statistic distribution derived from the Tsallis entropy.The total number of particles,the total energy,and the heat capacity at constant volume of the system are derived.The thermostatistic characteristics of the system are discussed in detail.It is found that the thermostatistic properties of such a system depend closely on parameter q,dimensional number of the space,kinetic characteristics of particles and shapes of the exteal potential,and the exteal potential has a great influence on the thermostatistic properties of the system.Moreover,it is shown that the results obtained here are very general and can be used to unify the description of the nonextensive and extensive thermostatistic properties of a class of Fermi systems trapped in different exteal potentials so that the important conclusions of many typical Fermi systems in the literature may be directly derived from the present paper.