A new green magnetic nanocatalyst was introduced for one-pot fast synthesis of propargylamine and triazole derivatives. Chitosan bio-polymeric chains were functionalized with polyvinyl alcohol (PVA) and then templated with silver nanoparticles (AgNPs) and magnetic Fe₃O₄ to obtain the AgNPs/Fe₃O₄@chitosan/PVA composite. Spectral and analytical examinations were conducted using X-ray diffraction, Fourier transform-infrared spectroscopy, scanning electron microscopy, transmission electron microscopy, vibrating sample magnetometry, and energy-dispersive X-ray spectroscopy for understanding the structural, morphological and physiochemical features of the obtained magnetic nanocomposite and the homogeneous distribution of AgNPs on the surface of nanocomposite with Fe₃O₄ nucleus. The AgNPs/Fe₃O₄@chitosan/PVA nanocatalyst was used in the synthesis of biologically active compounds such as propargylamine and triazole derivatives through multicomponent A³-coupling and click reactions. The catalyzed products were obtained in high yields under ambient conditions through a low-cost, facile, one-pot, and environmentally friendly protocol. The reusability of the heterogeneous magnetic catalyst was also confirmed up to six cycles without any significant loss in the catalytic activity, as well as easy separation of the catalyst.