Background and Objectives: The use of optical amplifiers in optical communications systems is currently of great interest. An optical signal can be amplified using semiconductor amplifiers, erbium or Raman amplifiers. Unfortunately, a linear laser amplifier adds spontaneous emission noise to the signal, degrading the signal-to-noise ratio. The use of phase-sensitive parametric amplifiers allows increasing the signal-to-noise ratio. Phase-sensitive amplifiers provide phase and amplitude squeezing that gives additional opportunities for signal regeneration and coding. Phase-sensitive amplification can be realized using four-wavemixing in highly nonlinear fibers. The resonant frequency for the parametric gain depends on the phase matching conditions for interacting waves. In real fibers, the resonant frequency is randomly shifted by fluctuations of the fiber dispersion. Dispersion fluctuation leadstothe degradation ofthe gain and narrowing ofthe gain bandwidth. Resonantfrequenciesforthe parametric gain can be extended using diameter modulation along the fiber length. Modulation of the fiber diameter gives rise to the modulation of the fiber dispersion. Periodic variation of the fiber dispersion leads to the excitation of the multipeak modulation instability spectrum. The signal wave can be amplified in modulation instability sidebands. Previous studies of the parametric gain in dispersion oscillating fibers are focused on the phase-insensitive amplification. In the present work, the phase-sensitive amplification in modulation instability sidebands is considered. Materials and Methods: We consider a truncated three-wave model for the parametric amplification of a continuous signal in the presence of strong single-frequency pump wave and weak idler wave. The dispersion and nonlinearity coefficients are calculated for the highly-nonlinear optical fiber with the W-shaped refractive index cross-section. Using numerical simulation, the gain coefficient for the signal wave was calculated in the terahertz frequency detuning range. Both the sine-wave modulation and the multi-frequency modulation of the fiber dispersion are considered. Results: We have found that the phase-sensitive amplification can be realized in high-order modulation instability sidebands. Single-frequency pump is sufficient to excite quasi-phase-matching sidebands. The amplification or depletion of the signal wave depends both on the individual phases of the interacting waves and on the phase of the dispersion oscillation. This effect makes it possible to manipulate the position of the depletion bands within the modulation instability sidebands. Resonant frequencies of the modulation instability sidebands depend on the modulation period. But the gain bandwidth depends on the type of modulation. Multifrequency modulation allows extending the gain bandwidth. We have found that high-order modulation instability sidebands can contain several narrow depletion bands, which frequency depends on the phases of the interacting waves and the phase of the dispersion oscillation. Conclusion: Modification of the phase-matching conditions in optical fibers with a variable dispersion allows improving the performance of parametric amplifiers. We have proposed the use of dispersion oscillating fiber for the generation of a comb of multiple spectral sidebands with phase-sensitive gain. When compared with the other possible schemes such as phase matching induced by the fourth-order dispersion coefficient, we expect that our proposed technique is more tolerant with respect to the longitudinal stochastic fluctuations of the fiber properties.