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The rich interplay of unconventional superconductivity and symmetry-breaking states lies at the frontier of physics and materials science. Here we report muon spin rotation (${\mu}$SR) experiments of the magnetic impurity effect on the superconducting and normal state properties in the prototypical kagome superconductor LaRu$_{3}$Si$_{2}$. In the normal state, zero-field ${\mu}$SR experiments reveal a hidden magnetism in the undoped system which is enhanced by Fe-doping. From measurements of magnetic penetration depth ${\lambda}$, doping induces a change of gap structure from nodeless $s$-wave to nodal gap symmetry. The $T_{\rm c}$/$\lambda^{-2}$ ratio is comparable to that of unconventional superconductors. Taken together, these results suggest unconventional superconducting and normal states in this kagome system.