This research investigates k-Almost Newton-Ricci solitons (k-ANRS) embedded in a metallic Riemannian manifold Mn having the potential function ψ. Furthermore, we prove geodesic and minimal conditions for hypersurfaces of metallic Riemannian manifolds. Beside this, we have explained some applications of metallic Riemannian manifold admitting k-Almost Newton-Ricci solitons.