<p>We investigate the characteristics and correlation between geometric parametric instability (GPI) sidebands and sidelobes in normally dispersive graded-index multimode fibers, where the core diameter is periodically modulated along the propagation direction. Theoretical simulations reveal that in addition to the standard GPI sidebands, a set of extra frequency peaks—GPI sidelobes—arises due to the Moiré modulation of the core diameters of the fiber and the breathing effects in multimode GRIN fiber. The exact frequency shift and strength of these sidelobes can be controlled by the amplitude and period of the fiber radius modulation. Through multiple spectral simulations conducted under initial noisy conditions, we demonstrate the energy correlation between the sidebands and sidelobes utilizing both scattergrams and a frequency-dependent energy correlation map. The results indicate that the conjugate sidebands and sidelobes exhibit a strong correlation, whereas other combinations show minimal correlation. Moreover, the variations in the core modulation period can alter the degree of correlation between the conjugate sidebands and sidelobes. A detailed discussion on the effects of other fiber core radius distribution profiles introduced by imperfect practical implementation is provided. These findings offer significant insights into the novel dynamical effects of GPI and facilitate the development of tunable multi-photon-pair-like light sources.</p>