In this research, we presented new types of modules, which are ℱ -extending modules,  ℱ-Goldie extending (ℱ-𝒢-extending module) and a unique ℱ-closure module (𝒰ℱ𝒞 -module), Which are generalizations for each of extending modules, Goldie extending module and a unique closure module.   In this work, we introduce a new type of modules that is ψF-G-extending modules and we define a module M is called ψF-G-Goldie-extending iff for all submodule 𝒱 of M that containing F, where 𝓗 ≤F⊕ M, F ≤ 𝓗  satisfies  and V ψF 𝓗. We provide many characteristics related to this kind. In a module M, we define the relationships on the group of submodules of M: i. Vψℱ B  iff 𝒦 ≤ M   satisfies 𝒱 ≤ℱE 𝒦 and  B ≤ℱE 𝒦.  ii. Vφℱ B iff  𝒱 ∩ B ≤FE 𝒱 and 𝒱 ∩ B ≤FE B. A module ℳ is called ℱ -Goldie extending (ℱ-𝒢-extending module) if for every 𝒱 ≤ ℳ that contains ℱ, where a ℱ-direct summand 𝓗 of ℳ satisfies ℱ ≤ 𝓗 and 𝒱 φℱ 𝓗  and we introduce some Characteristics and Features for this kind module.