  We present results of specific heat, electrical resistance, and
magnetoresistivity measurements on single crystals of the heavy-fermion
superconducting alloy Ce$_{0.91}$Yb$_{0.09}$CoIn$_5$. Non-Fermi liquid to Fermi
liquid crossovers are clearly observed in the temperature dependence of the
Sommerfeld coefficient $\gamma$ and resistivity data. Furthermore, we show that
the Yb-doped sample with $x=0.09$ exhibits universality due to an underlying
quantum phase transition without an applied magnetic field by utilizing the
scaling analysis of $\gamma$. Fitting of the heat capacity and resistivity data
based on existing theoretical models indicates that the zero-field quantum
critical point is of antiferromagnetic origin. Finally, we found that at zero
magnetic field the system undergoes a third-order phase transition at the
temperature $T_{c3}\approx 7$ K.
