Grafting 6-aminopenicillanic acid (6-APA) onto superparamagnetic γ-Fe₂O₃@SiO₂ nanocomposites led to the production of 6-APA/γ-Fe₂O₃@SiO₂ as a novel heterogeneous nanocatalyst. Protonation and deprotonation of 6-APA/γ-Fe₂O₃@SiO₂ nanocomposites were investigated using quantum mechanical calculations. The behaviour of bifunctionality on this catalyst was examined and the results showed that it acts as an acid–base bifunctional system, and the reaction proceeds very well under mild and ambient conditions. The deprotonation of the COOH group is easier than the NH and NH₂ groups with respect to the energy data and the results of the molecular electrostatic potential (MEP) analyses. In the presence of the nanocomposite, the protonation of the NH₂ group is more favourable than the NH group. It was characterized by powder X-ray diffraction (XRD), scanning electron microscopy (SEM), transmission electron microscopy (TEM), energy dispersive spectroscopy (EDS), vibrating sample magnetometery (VSM), thermo-gravimetric analysis (TGA), and Fourier transform infrared spectroscopy (FT-IR). This reaction is not only kinetically stable but is also a spontaneous reaction and thermodynamically favored. The superparamagnetic nanocomposite was used in the preparation of 1,4-dihydropyrano[2,3-c]pyrazole derivatives under a one-pot multicomponent reaction. The nanocomposite was recyclable for at least 10 cycles without any loss in the activity.