In this paper, we introduce the concept of n-IFP-flat (respectively, n-IFP-injective) modules as nontrivial generalization of flat (respectively, injective) modules. We first investigate various properties of these modules. For example, we show that over any ring R, every R-module has an IF n-preenvelope, where IF n is class of all n-IFP-flat right R-modules. Secondly, we investigate the existence of n-IFP-injective covers. It is shown that over any ring R, n-IFP-injective cover always exists. Finally, we show that (IFn,IF⊥n) is a perfect cotorsion theory. © 2017 World Scientific Publishing Company.