In this paper, a novel polyamide containing pyrimidine and methine thiophene linkages (poly(pyrimidine-thiophene-amide) (P(P-T-A))) was synthesized. Then, the magnetic calcium alginate nanocomposite containing P(P-T-A) (CA-P(P-T-A)-Ni0.2Zn0.2Fe2.6O4 (NZFO)) was synthesized for studying neodymium (Nd+3), terbium (Tb+3), and dysprosium (Dy+3) ions adsorption in the single ion solutions. The obtained results of X-ray diffraction (XRD), field emission scanning electron microscope (FE-SEM), energy-dispersive X-ray (EDX), nuclear magnetic resonance (NMR), thermogravimetric analysis (TGA), vibrating sample magnetometer (VSM), and Fourier transform infrared (FT-IR) indicated the successful synthesis of the materials. The value of saturation magnetization of the nanocomposite was reported to be 15.28 emu/g, indicating an appropriate magnetic response. Under the optimum conditions, adsorption efficiency for Nd+3, Tb+3, and Dy+3 was 96.73, 94.82, and 97.58 %, respectively. According to the experimental results, it can be stated that the data of REEs adsorption were efficiently fitted by nonlinear pseudo-second-order kinetic model. Adsorption isotherms were also evaluated by fitting with Freundlich and Langmuir isotherm models. A better fit was achieved by Freundlich model in the case of Tb+3 and Dy+3 ions, while Langmuir isotherm fitting reported a better result for Nd+3 adsorption data. Moreover, the changes in Gibbs free energy (ΔG°), enthalpy (ΔH°), and entropy (ΔS°) values presented a feasible and endothermic ions adsorption process onto the nanocomposite that occurred spontaneously under the investigated conditions. The obtained results indicated that the nanocomposite can be considered as a potential adsorbent for the efficient adsorption of the investigated ions.