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The main purpose of the paper is to prove that if a compact Riemannianmanifold admits a gradient $\rho$-Einstein soliton such that the gradientEinstein potential is a non-trivial conformal vector field, then the manifoldis isometric to the Euclidean sphere. We have showed that a Riemannian manifoldsatisfying gradient $\rho$-Einstein soliton with convex Einstein potentialpossesses non-negative scalar curvature. We have also deduced a sufficientcondition for a Riemannian manifold to be compact which satisfies almost$\eta$-Ricci soliton (see Theorem 2).

Some results on $\eta$-Ricci Soliton and gradient $\rho$-Einstein soliton in a complete Riemannian manifold