Abstract. In the present work, we explore how a Fermionic interaction potential having the form of a power-law affects the EoS parameter in the cosmological model with Fermionic field, proposed by us earlier. It is found that, for a range of model parameter values, the EoS parameter of the dark energy field is practically constant, with a value nearly equal to -1. This value is consistent with what we expect from observations. From the nature of the behavior of the EoS parameter, it is concluded that the current model can be treated like a cosmological constant for a range of model parameter values.