  The effects of structural quantum criticality on the strong-coupling
superconductivity of (Sr$_{1-x}$Ca$_x$)$_3$Rh$_4$Sn$_{13}$ have been
investigated via electrical resistivity and specific heat measurements. We
demonstrate that the lattice specific heat at low temperatures considerably
increases toward the structural quantum critical point (SQCP), $x_{\rm
c}\approx0.9$. The superconducting gap increases with $x$ in the exact same
fashion as the low-temperature lattice specific heat, clearly indicating that
the abundant low-energy phonons cause strong-coupling superconductivity.
Despite the electron-phonon interaction, which is much more enhanced than the
electron correlation, the low-temperature electrical resistivity near the SQCP
varies as $\propto T^2$. This finding suggests that structural quantum
fluctuation affects the power law arising from the electron-phonon scattering.
