<p>In most studies concerning soliton solutions, solitons typically propagate on a constant background. Nevertheless, backgrounds are generally not constant in practical situations, which makes the study of soliton on periodic background solutions the main purpose of this paper. By employing the Kadomtsev-Petviashvili (KP) hierarchy reduction method and the Hirota bilinear technique, we construct soliton on periodic background solutions for the generalized coupled nonlinear Schrödinger (GCNLS) system. These solutions are further expressed in terms of Gram-type determinants. The dynamical behaviors and characteristics of these solutions are analyzed via 3D, 2D and density plots. For the two-soliton solutions, adjusting parameters allows switching among dark-bright, dark-dark, and bright-bright soliton structures. For periodic solutions, adjusting parameters leads to remarkable changes in the solution profiles, while the two components exhibit nearly synchronized periods. For soliton on periodic background solutions, the dark-bright soliton solutions and periodic solutions interact with each other, and variations in parameters can lead to the degeneration of the periodic background as well as regulate the shape of solitons. We gradually construct soliton solutions, periodic solutions and soliton on periodic background solutions for the GCNLS system. These solutions are applicable to optics, fluid mechanics, plasma physics and other nonlinear science fields, and support the development of nonlinear wave theory.</p>