We report the evidence of plasmonic-photonic resonances in hybrid metallo-dielectric quasi-crystal nanostructures composed of aperiodically-patterned low-contrast dielectric slabs backed on a metal layer. Via both experimental and numerical studies, we characterize these resonant phenomena with specific reference to the Ammann-Beenker (quasiperiodic, octagonal) tiling lattice geometry, and investigate the underlying physics. In particular, we show that, by comparison with standard periodic structures, a richer spectrum of resonant modes may be excited. Such modes are characterized by a distinctive plasmonic or photonic behavior, discriminated by their field distribution. Concerning the possible applications, we also explore the structure functionalization via nanosized high refractive index overlays (for resonance tuning and quality-factor enhancement), as well as its surface sensitivity to deposition of …