Abstract: In the frontier field of nuclear physics, the interaction between vortex γ photons and nucleus has emerged as a captivating research direction, particularly due to the unique orbital angular momentum (OAM) carried by vortex photons. Unlike conventional plane-wave photons, vortex γ photons exhibit distinct concentric ring transverse intensity distributions and helical phase structure, leading to fundamentally different interaction mechanisms with nuclear systems. When a nucleus is aligned along the incident axis of a vortex γ photon, the photon’s OAM significantly changes nuclear transition selection rules, enabling selective excitation and extraction of specific multipole giant resonances phenomena typically constrained by dipole-dominated selection rules in plane-wave interactions. A critical parameter governing this interaction is the impact parameter b, defined as the transverse distance between the vortex γ photon’s incident axis and the nucleus. Compared to plane-wave photons, the annular intensity profile of vortex photons results in a strong dependence of photon absorption cross-sections on b. This necessitates a systematic investigation of how target spatial distributions modulate cross-sections and transition rules during vortex-nucleus interactions. In this study, the interaction of vortex γ beams with mesoscopic nuclear targets characterized by Gaussian spatial distributions was theoretically analyzed. Our findings reveal distinct mechanisms in the giant resonance energy region. When the mesoscopic nucleus target coincides with the vortex beam axis, for the target whose width is smaller than the wavelength of the incident photon, the absorption cross sections of the vortex γ photon begin to appear a suppression effect relative to plane-wave predictions. As the target width increases, the suppression diminishes, and the absorption cross-section of vortex γ photons at the same multipolar L transition is 1/\mathrmcos\;\theta _k as large as the plane-wave result and \theta _k is the polarization angle of the vortex γ photon. When the target and the vortex γ beam axis do not coincide, if the width of the nucleus target distribution w is smaller than the transverse size of the photon, it can be observed that the photoabsorption cross section is affected by the transverse structure of the vortex γ photon, and there is an obvious vortex effect. Similar conclusions can be drawn for transitions with higher multipolarity L. Therefore, through the vortex γ photon, we can realize the regulation of the giant multipole resonances of the mesoscopic nucleus target and can recognize the selective absorption of the nucleus target to different angular momentum photons in the beam. The above results will provide theoretical guidance and parameter support for the in-depth understanding of the interaction between the vortex γ photons and the nucleus and the regulation study.