In this work, we consider the preparation of magnetic magnetite nanoparticles (MNPs, Fe3O4)) by chemical precipitation method, modified with biocompatible polymers such as polyethyleneimine (PEI) and chitosan (CS) to get Fe3O4@PEI and Fe3O4@CS, respectively, alongside electrospun polyamide (PA) nanofibers and their sorption properties towards some of the synthetic food azo dyes (Tartrazine (TRT), Sunset Yellow FCF (SY), Azorubine (AR), and Ponceau 4R (P-4R)). Spherical MNPs (7.5 ± 0.2 nm, TEM) and PA electrospun nanofibers (52 ± 3 nm to 104 ± 11 nm, SEM) were prepared, with a specific surface area of 101 m2 g−1 (MNPs) and 44 m2 g−1 (PA). The pore space volume of PA nanofibers was 0.024 cm3 g−1 which is much less than for MNPs (Fe3O4, 0.282 cm3 g−1; Fe3O4@CS, 0.218 cm3 g−1; and Fe3O4@PEI, 0.154 cm3 g−1). The saturation magnetization of Fe3O4@CS (40 emu g−1) and Fe3O4@PEI (43 emu g−1) was slightly lower than that of Fe3O4 (48 emu g−1). Sorption studies under optimized conditions (pH, time, sorbent mass) achieved 95–99% dye recovery. The kinetics of dye sorption was studied, and pseudo-second-order of sorption was preferable. For Fe3O4@PEI, the maximum sorption capacity (qmax, mg g−1) values increased to 150 (SY), 151 (AR), 176 (TRT), and 204 (P-4R); for Fe3O4@CS, 57 (SY), 104 (TRT), 139 (P-4R), and 142 (AR); and for PA, 28 (Ar), 31 (TRT), 33 (P-4R), and 39 (SY) within the Langmuir model. The difference in sorption capacity and recovery may be attributed to steric factors and the chemical structure of the azo dye molecule.