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Ferrite nanoparticles of Ni${}_{0.35}$Mn${}_{0.35}$Zn${}_{0.3}$Fe${}_{2-x}$Ce_xO₄ ferrite system were produced using sol–gel auto combustion technique. X-ray diffraction analysis confirms the single phase cubic spinel structure of the samples with space group Fd-3m. Replacement of Fe${}^{3+}$ ions by Ce${}^{3+}$ ions increases the lattice parameter 8.4105 Å to 8.4193. Average crystallite size obtained from Scherrer method varies from 21.73nm to 22.71nm with replacement of Fe${}^{3+}$ ions by Ce${}^{3+}$ ions. Williamson–Hall and strain-size plot analysis confirms the nanocrystalline nature of the samples and the micro-strain induced in the cubic crystals is of tensile type. Cation distribution suggests that Zn${}^{2+}$ ions occupy tetrahedral — A-site while Ni${}^{2+}$ ions occupy octahedral — B-site. Majority of the Mn${}^{2+}$ ions prefer A-site and majority of the Ce${}^{3+}$ ions replace Fe${}^{3+}$ ions at octahedral — B-site. High resolution transmission images confirm the homogeneity and nanoparticle nature of the samples. Two main characteristics absorption bands corresponding to spine structure are observed in the Fourier transmission infra-red spectra within the wavenumber range of 350–600cm${}^{-1}$. Stiffness constant, Young’s modulus, rigidity modulus, bulk modulus and Debye temperature were estimated using FTIR data. Debye temperature obtained from the Waldron equation varies from 676K to 692K with the addition of Ce${}^{3+}$ ions. Higher values of elastic moduli are suitable for industrial applications due to increased mechanical strength.