  The hybrid skin-topological effect (HSTE) in non-Hermitian systems exhibits
both the skin effect and topological protection, offering a novel mechanism for
the localization of topological edge states (TESs) in electrons, circuits, and
photons. However, it remains unclear whether the HSTE can be realized in
quasicrystals, and the unique structure of quasicrystals with multi-site cells
may provide novel localization phenomena for TESs induced by the HSTE. We
propose an eight-site cell in two-dimensional quasicrystals and realize the
HSTE with eight-site nonreciprocal intracell hoppings. Furthermore, we can
arbitrarily adjust the eigenfield distributions of the TESs and discover domain
walls associated with effective dissipation and their correlation with
localization. We present a new scheme to precisely adjust the energy
distribution in non-Hermitian quasicrystals with arbitrary polygonal outer
boundaries.
