This paper focus on semi-conjugate connections of affine connections on metallic pseudo-Riemannian manifolds, with particular attention to their relation with twin metrics, Codazzi coupling, and torsion tensors. The study is useful for giving a better understanding of the geometric behavior of these manifolds and also the role played by semi-conjugate connections in differential geometry. This study mainly include a theoretical method, based on several definitions and theorems, to obtain necessary and sufficient conditions for F-connections, relations involving h-semi-conjugate and H-semi-conjugate connections, and equivalent conditions connected with Codazzi-coupled pairs. A concrete example is also presented at the end to support the theoretical results. Among the main findings, the paper gives conditions under which semi-conjugate connections can be considered as F-connections and explains how such connections are related with torsion tensors. The results also indicate that Codazzi coupling has an important role in determining the symmetry and structure of these connections. The results describe how semi-conjugate connections behave in metallic pseudo-Riemannian geometry and provide a starting point for further investigations of related affine structures.