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Let M be a module, and let U, V, F be submodules of M with F proper. We say V is an F-supplement of U in M if it is minimal in the collection of submodules such that . If every cofinite submodule of M has an (ample) F-supplement, then we call M a (amply) cofinitely F-supplemented module. We give some general properties of these modules, and we characterize them in terms of their certain submodules.