A fermionic deformation scheme is applied to a study on the low-temperature quantum statistical behavior of a quasifermion gas model with intermediate statistics. Such a model does not satisfy the Pauli exclusion principle, and its quantum statistical properties are based on a formalism of the fermionic q-calculus. For low temperatures, several thermostatistical functions of the model such as the chemical potential, the heat capacity, and the entropy are derived by means of a function of the model deformation parameter q. The effect of fermionic q-deformation on the low-temperature thermostatistical properties of the model are discussed in detail. Our results show that the present deformed (quasi)fermion model provides remarkable connections of the model deformation parameter q, first, with the thermal effective mass of a quasiparticle, and second, with the temperature parameter. Hence, it turns out that the model deformation parameter q has also a role controlling the strength of effective quasiparticle interactions in the model. Finally, we conclude that this work can be useful for understanding the details of interaction mechanism of fermions such as quasiparticle states emergent in the fractional quantum Hall effect. (C) 2015 Elsevier B.V. All rights reserved.