Correlation effect may be induced by the flat band(s) near the Fermi energy, as demonstrated in twisted graphene, Kagome materials, and heavy Fermion materials. Unconventional superconductivity may arise from this correlation effect and show deviation from the phonon-mediated pairing as well as the Landau Fermi liquid in the normal state. Here, we report the anomalous properties in normal and superconducting states in the Laves phase superconductor Sc2Ir4-xSix with a kagome lattice and silicon doping. By doping silicon to the iridium sites, a phase diagram with nonmonotonic and two-dome-like doping dependence of the superconducting transition temperature Tc was observed. The samples in the region of the second dome, including Sc2Ir3.5Si0.5 with the optimal Tc, exhibit non-Fermi liquid behavior at low temperatures after superconductivity is suppressed, as evidenced by the divergence of the specific heat coefficient and the semiconducting-like resistivity, together with a strong superconducting fluctuation in the optimally doped samples. Combined with first-principles calculations, we attribute the anomalous properties in normal and superconducting states to the correlation effect, which is intimately induced by the flat band effect when considering the strong spin-orbit coupling.
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