In this work, cofinitely \(\oplus -g-\) supplemented modules are defined and some properties of these modules are investigated. It is proved that any direct sum of cofinitely \(\oplus -g-\) supplemented modules is also cofinitely \(\oplus -g-\) supplemented. Let M be a distributive and cofinitely \(\oplus -g-\) supplemented \(R-\) module. Then, every factor module and every homomorphic image of M are cofinitely \(\oplus -g-\) supplemented. Let M be a cofinitely \(\oplus -g-\) supplemented \(R-\) module with \(\left( D3\right) \) property. Then, every cofinite direct summand of M is cofinitely \(\oplus -g- \) supplemented. Let M be an \(R-\) module with SSP property. Then, every cofinite essential submodule of M has a g-supplement that is a direct summand in M if and only if every essential maximal submodule of M has a g-supplement that is a direct summand in M.
