<p>The present study investigates the effect of Y³⁺ and Cr³⁺ co-doping on the crystal structure, vibrational, elastic, morphological and magnetic properties of CoFe_2−xY_x/2Cr_x/2O₄ (x = 0.00, 0.02, 0.04, 0.06, 0.08, 0.10.) nanoparticles synthesized via cost-effective sol-gel auto-combustion method ensuring high purity. The nanoparticles were synthesized in nano-sized dimension using sol-gel auto-combustion method. All the synthesized nanoparticles show single phase nature associated with cubic spinel structure which was well supported by Rietveld analysis. The Rietveld refinements exhibited a better goodness of fit (χ²) between 2.54 and 2.64. The lattice constant decreases from 8.387 Å to 8.380 Å on doping Y³⁺ and Cr³⁺ ions. The crystallite size obtained from Scherrer’s equation is in the range of 23&#xa0;nm to 18&#xa0;nm. Cation distribution obtained from XRD method and Rietveld method suggests occupancy of Y³⁺, Cr³⁺, Co²⁺ ions at octahedral [B] site while Fe³⁺ ions get distributed over tetrahedral (A) and octahedral [B] sites. FTIR spectra show the absorption bands near 400&#xa0;cm^− 1 to 550&#xa0;cm^− 1 characterizing the spinel nature. The vibrational and mechanical properties like Debye temperature, stiffness constant, Young’s modulus, bulk modulus, modulus of rigidity increases marginally on doping of Y³⁺ and Cr³⁺ ions. Raman spectra characterizes the formation of spinel ferrite structure. The surface morphology was viewed through Scanning Electron Microscopy (SEM) technique which show dense morphology with grain size in the range of 21&#xa0;nm to 25&#xa0;nm. The saturation magnetization (Ms) linked with the A-B superexchange interaction decreased with Y³⁺ and Cr³⁺ ions. The coercivity (Hc) initially increases and then decreases with Y³⁺ and Cr³⁺ ions within the doping level of x = 0.00 to 0.10.</p>