In this paper, the authors generalize the notions of pseudo injective module and C-injective module and define, for an \(R\)-module \(M\), \(M\)-C-injective modules and study their properties. The authors give an example to show that \(M\)-C-pseudo injectivity does not imply \(M\)-pseudo injectivity. If an \(R\)-module \(M\) is \(M\)-C-pseudo injective the authors call \(M\) a C-pseudo injective. They prove that a commutative ring \(R\) is semisimple Artinian if and only if the direct sum of any two C-pseudo injective \(R\)-modules is C-pseudo injective. In Proposition 2.20, the authors prove that every C-pseudo injective, directly finite module is co-Hopfian. This proof doesn’t seem to be okay as here \(\alpha\) may not be closed, that is, \(\alpha(M)\) may not be closed in \(M\). The proof of Proposition 2.24 does not use the hypothesis that \(M\) is C-pseudo injective. The authors prove that every pseudo injective ring is equal to its classical quotient ring. The proof of the authors’ last result (Proposition 2.31) doesn’t seem to be okay as \((f-g)(x)r=0\Rightarrow (f-g)(x)=0\) is not clear. Also \(\text{Ker}(f)\subseteq\text{Ker}(fh)\) is not clear.