Abstract <p>The spectrum of the high harmonics generated by a Ga⁺ ion exposed to an intense femtosecond laser pulse simultaneously with short-wavelength radiation whose frequency is multiple of the fundamental harmonic and intensity is much lower than the laser intensity has been theoretically investigated. The calculation results show significant enhancement of the radiation of the odd harmonic that is in a multiphoton resonance with the transition from the ion ground state to the autoionizing state 3<i>d</i>⁹4<i>s</i>²4<i>p</i>&#xa0;¹<i>P</i>₁ and single-photon resonance for the short-wavelength radiation with an increase in its intensity to 10⁹ W/cm². The effect of the enhancement due to the single-photon resonant pump may explain the resonant enhancement of the harmonic observed in experiments with a gallium plasma target.</p>