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The effect of the substitution of Fe atoms by Ni atoms on the spin-modulated spatial structure (SSMS) and hyperfine interactions of 57Fe nuclei in the BiFeNiO3 multiferroic has been studied using Mössbauer spectroscopy methods in a wide temperature range (5-700 K), including the temperature of the magnetic phase transition. It is established that at temperatures below the Néel temperature an incommensurate anharmonic SSMS of cycloid type is formed by magnetic moments of iron atoms with different cationic surroundings. When the Fe atoms are replaced by Ni atoms, the SSMS anharmonicity parameter increases. The appearance of the Ni atom in the nearest cationic environment of the Fe atom leads to a decrease of the isotropic contribution to the hyperfine magnetic field but does not lead to a noticeable change in the anisotropic contribution, and also the quadrupole shift and shift of the Mössbauer line.