  In this paper we introduce and characterize a pseudo generalized
Ricci-recurrent spacetimes and produce an example to verify the existence of
such a spacetime. Then we demonstrate that a conformally flat generalized
Ricci-recurrent spacetime with certain condition is a pseudo quasi-Einstein
spacetime. Besides, it is proved that a pseudo generalized Ricci-recurrent
generalized Robertson-Walker spacetime represents a perfect fluid spacetime.
Lastly, we study the impact of this spacetime under $f(\mathcal{R},T^2)$ and
$f\left(\mathcal{R}^{\ast}\right)$ gravity scenario and deduce several energy
conditions.
