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It is known that magnetite Fe3O4 nanoparticles are the most acceptable material for application in cell separation, drug delivery, hyperthermia and as a contrast material in magnetic resonance imaging MRI. The inverse spinel structure of magnetite is very flexible and can absorb a huge variety of ions on several crystallographic positions (on the [B] and (A) crystal sites). Magnetic structure of spinels can be varied in a wide range from ferro-, ferri-, and antiferromagnetic to canted and frustrated magnetic structure in the case of disordered state of magnetic ions. Thus, the properties of cubic spinel nanomaterials can be tuned, by replacing the different ions (Co2+, Ga3+, Ni2+, Cr3+, Mn2+ and others) on the [B] and (A) crystal sites. Here we report on synthesis of Fe1+xGa2-xO4 nanoparticles with cubic spinel structure by combustion method. The physical properties of the materials were studied by a complex methods, such as XRD, TEM, electron diffraction, EDX, Magnetic measurements, Raman and Mössbauer spectroscopy in temperature range 10 – 300 K. XRD and electron diffraction revealed that the samples have the cubic spinel-type structure (sp. gr. Fd3m) with an average nanoparticles size of 28.0 nm. Mössbauer spectroscopy was used to evaluate the iron valence and spin states, the magnetic ordering temperature, phase composition of the sample and cation distribution. Basing on XRD, Raman and Mössbauer spectroscopy data we concluded that not only FeGa2O4 phase but a new phase γ-FeGaO3 similar to cubic spinel γ-Fe2O3 and γ-Ga2O3 is presented in their samples. The low temperature Mössbauer data revealed that Fe1+xGa2-xO4 nanoparticles is non-homogeneous magnetic system with frustrated interactions specific of spin-glasses with ordering temperature at about 26 K. The transformation of the shape of low temperature paramagnetic Fe2+ doublet components was found under heating from 30 K to room temperature. This transformation occurs due to unusual temperature behavior of the Fe2+ ion quadrupole splitting at tetrahedral sites, which was initiated by the Jahn-Teller effect. The distortions of tetrahedral Fe2+ iron environment due to JT effect was found in many spinels containing Fe2+ ions in tetrahedral coordination, however, to our knowledge, this effect was not observed in bulk FeGa2O4 material. Support by the Russian Scientific Foundation (Project #14-12-00848) is acknowledged.