  A magnetic order can be completely suppressed at zero temperature($T$), by
doping carriers or applying pressure, at a quantum critical point(QCP), around
which physical properties change drastically. However, the situation is unclear
for an electronic nematic order that breaks rotation symmetry. Here we report
nuclear magnetic resonance(NMR) studies on NaFe$_{1-x}$Co$_{x}$As where
magnetic and nematic transitions are well separated. The NMR spectrum is
sensitive to inhomogeneous magnetic fields in the vortex state, which is
related to London penetration depth $\lambda_{\rm L}$ that measures the
electron mass $m^*$. We discovered two peaks in the doping dependence of
$\lambda_{\rm L}^2$($T\sim$0); one at $x_{\rm M}$=0.027 where the spin-lattice
relaxation rate shows quantum critical behavior, and another at $x_{\rm
c}$=0.032 around which the nematic transition temperature extrapolates to zero
and the electrical resistivity shows a $T$-linear variation. Our results
indicate that a nematic QCP lies beneath the superconducting dome at $x_{\rm
c}$ where $m^*$ is enhanced. The impact of the nematic fluctuations on
superconductivity is discussed.
