The material properties of quasicrystals are significantly affected by defects due to high brittleness. Understanding the fracture behavior of quasicrystals is crucial for material applications. In this paper, the fracture mechanics of one-dimensional hexagonal quasicrystals with periodic Type-III multiple cracks emanating from a nanoscale hole is investigated theoretically. Based on complex elasticity theory and the Gurtin-Murdoch surface elasticity theory, stress fields of a nano-hole with periodic multiple cracks, considering surface effects, are obtained using boundary value problems of analytic function theory and the conformal transformation technique. Analytical expressions for stress intensity factors and energy release rates of the phonon field and phase field at the crack tip under the same conditions are further derived. The effects of aperture size, number of periodic cracks, crack-length/aperture ratio, coupling coefficient between phonon field and phase field, and applied loads on dimensionless stress intensity factors and dimensionless energy release rate are discussed. Results indicate that the coupling coefficient, applied loads, and aperture size do not affect dimensionless stress intensity factors without surface effects. Larger aperture sizes show stronger size dependence on dimensionless stress intensity factors and dimensionless energy release rate when considering surface effects. An obvious coupling effect between the phonon field and the phase field is observed. The influence of the number of periodic cracks on dimensionless stress intensity factors and energy release rate is restricted by defect size. The effects of phonon field loads and phase field loads on dimensionless stress intensity factors and energy release rate differ. This work reveals the specific influence of surface effects on the fracture behavior of multi-cracks at the hole edge, offering significant academic insights into quasicrystal fracture mechanics.