<p>We investigate the anharmonic oscillation in the modulated fractional diffraction system with harmonic-oscillator potential. By deriving explicit analytical solutions, we elucidate the evolution of Gaussian beam within the framework of the fractional Schrödinger equation with a longitudinally modulated harmonic-oscillator potential. The analysis reveals that the anharmonic oscillation amplitude, evolution velocity, beam width and amplitude distribution are significantly influenced by the Lévy index, initial transverse displacement, and chirp. Notably, Lévy index governs the anharmonic oscillation amplitude and evolution velocity of the Gaussian beam and a larger Lévy index induces the formation of oscillation in real space. The initial transverse displacement shifts the evolution trajectory, whereas the initial chirp dictates the beam width and amplitude distribution in both momentum and real spaces. Furthermore, we explore the impact of various longitudinal modulations on anharmonic oscillation and unveil a novel method for the direct generation of Airy-like pattern. This study provides an insight into the intricate dynamics of modulated fractional diffraction systems and offers a pathway for the special optical pattern generation.</p>