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Conventional two-dimensional (2D) higher-order topological insulators are characterized by higher-order topological states at the outer boundary of non-trivial regions, that is, 0D topological corner states (TCSs). In this Letter, it is found that the higher-order topological quasicrystalline insulators (HOTQIs) have non-0D TCSs arrays at the outer and inner boundaries, which breaks through the limitation of bulk-edge-corner correspondence (corresponding dimension is 2D-1D-0D). The universal theoretical framework of the multimer analysis method is improved and the difference in the average charge density is proposed as the real-space topological index, which effectively characterizes the unconventional higher-order topology in HOTQIs. Furthermore, HOTQIs and their non-0D TCSs arrays in photonic system are experimentally observed for the first time. These results offer a promising avenue for investigating TCSs with high integration and multi-region distribution and pave the way for exploring the topological phenomena and applications of photonic and phononic quasicrystals.