Cobalt-, zinc-, and nickel-zinc-substituted nano-size manganese ferrite powders, $MnFe_2O_4$, $Mn_{0.8}Co_{0.2}Fe_2O_4$, $Mn_{0.8}Zn_{0.2}Fe_2O_4$ and $Mn_{0.8}Ni_{0.1}Zn_{0.1}Fe_2O_4$, were fabricated using a sol-gel method, and their crystallographic and magnetic properties were subsequently studied. The $MnFe_2O_4$ ferrite powder annealed at temperatures above 523 K exhibited a spinel structure, and the particle size increased as the annealing temperature increased. All ferrites annealed at 773 K showed a single spinel structure, and the lattice constants and particle size decreased with the substitution of Co, Zn, and Ni-Zn. The $M{\ddot{o}}ssbauer$ spectrum of the $MnFe_2O_4$ ferrite powder annealed at 523 K only showed a doublet due to its superparamagnetic phase, and the $M{\ddot{o}}ssbauer$ spectra of the $MnFe_2O_4$, $Mn_{0.8}Co_{0.2}Fe_2O_4$, and $Mn_{0.8}Zn_{0.2}Fe_2O_4$ ferrite powders annealed at 773 K could be fitted as the superposition of two Zeeman sextets due to the tetrahedral and octahedral sites of the $Fe^{3+}$ ions. However, the $M{\ddot{o}}ssbauer$ spectrum of the $Mn_{0.8}Ni_{0.1}Zn_{0.1}Fe_2O_4$ ferrite powder annealed at 773 K consisted of two Zeeman sextets and one quadrupole doublet due to its ferrimagnetic and paramagnetic behavior. The area ratio of the $M{\ddot{o}}ssbauer$ spectra could be used to determine the cation distribution equation, and we also explained the variation in the $M{\ddot{o}}ssbauer$ parameters by using this cation distribution equation, the superexchange interaction and the particle size. Relative to pure $MnFe_2O_4$, the saturation magnetizations and coercivities were larger in $Mn_{0.8}Co_{0.2}Fe_2O_4$ and smaller in $Mn_{0.8}Zn_{0.2}Fe_2O_4$, and $Mn_{0.8}Ni_{0.1}Zn_{0.1}Fe_2O_4$. These variations could be explained using the site distribution equations, particle sizes and magnetic moments of the substituted ions.