First, this work examines the structural characteristics of the formation of a ZnSeTe solid solution. Further, after the introduction of Fe substitution impurity, electronic energy spectra and densities of electronic states were calculated. Significant changes in parameters of the electronic structure and magnetic properties caused by external hydrostatic pressure were revealed. It was found that the doped solid solution of ZnFeSeTe under normal conditions is a semiconductor for both spin orientations. However, under the action of hydrostatic pressure, this material turns into a metallic state, since the 3d states of iron are now at the Fermi level. Under the influence of pressure, the magnetic moment of the supercell decreases by more than six times, that is, from 4.0 to 0.67 Bohr magnetons.