Due to their high variability and extraordinary features, the MOF-based nanomaterials are regarded as promising photocatalysts in organic reactions. In this study, the magnetic Co-MOF-based nanocomposite (denoted by Cys-CoFe/HK) was prepared through a facile sonochemical method. The composite design was based on the integration and synergy of the desired properties of the components, i.e., optical properties of the magnetic substrate and its separation capability, desirability of metal-organic framework to promote A3-coupling reaction, and use of cysteine amino acid as a natural modifier to modify nanoparticles and make an efficient charge transfer. The information about their structural features was obtained using various characterization methods. In addition to the high photocatalytic activity of the developed composite in the aerobic oxidative propargylic functionalization of styrene under visible light illumination, the composite showed a high capability to interact with a wide range of amines, styrene, and terminal alkynes as participants in A3-coupling reaction. Furthermore, the developed catalyst demonstrated high accessibility of active sites, reusability, and magnetic properties, which accelerated the efficiency of the A3-coupling reaction. Moreover, the mechanistic investigations, including trapping experiments, confirmed the presence of superoxide radical (O2●) and holes (h+) as essential species to perform the considered reaction. Our methodical approach to the fabrication of Cys-CoFe/HK composite provided optimal conditions for improving previous studies and thus the industrial processes in environmentally sensitive areas.