It has been shown that oxides containing multiple transition elements with near equi-atomic compositions have a strong tendency to crystallize into a single phase via configurational entropy. In this regard, we have synthesized and stabilized a new composition in nano- and bulk forms via chemical co-precipitation and standard solid-state reaction methods, respectively. The crystal structures of the synthesized samples crystallize in a pure spinel phase as confirmed by x-ray diffraction patterns. We have adopted different characterization techniques to investigate the structural, magnetic, and optical properties of samples prepared by different routes. We have investigated their dynamical behavior extensively by performing ac susceptibility measurements under different ac frequencies, magnetic memory effect in the negative and positive cycles under different temperatures and fields, thermoremanent magnetization, and aging effect. We have analyzed and fitted the frequency dependence of the freezing temperature using empirical laws, namely the Néel-Arrhenius law, the Vogel-Fulcher law, and the power law. The sample prepared by the coprecipitation technique exhibits a cluster spin-glass-like state as realized from the Mydosh parameter, relaxation time, and critical exponent. In contrast, this behavior is absent in the sample prepared by the solid-state reaction method. Furthermore, we have investigated the magnetic memory effect in the annealed samples and found that the nanosized samples exhibit a pronounced memory effect, which typically weakens as particle size increases towards the bulk regime. The obtained results of the memory effect are consistent with a hierarchical model of spin-glass. We have been able to determine the correct ground state for the inverse spinel structure using GGA+ and hybrid exchange-correlation functionals, which agrees well with our experimental outcomes. Further, we have correlated our theoretical results from some spectroscopic measurements such as x-ray photoelectron spectroscopy, UV-Visible-NIR spectroscopy, and ultraviolet photoelectron spectroscopy. Our combined experimental and theoretical study provides new insights that significantly broaden the understanding of entropy-stabilized spinels and their applications in the field of magnetic storage.