  We study the evolution of the Kondo effect in heavy fermion compounds,
Yb(Fe$_{1-x}$Co$_{x}$)$_{2}$Zn$_{20}$ (0$\leqslant$ x $\leqslant$ 1), by means
of temperature-dependent electric resistivity and specific heat. The ground
state of YbFe$_2$Zn$_{20}$ can be well described by a Kondo model with
degeneracy $N$ = 8 and a $T_K\sim$30 K. In the presence of a very similar total
CEF splitting with YbFe$_2$Zn$_{20}$, the ground state of YbCo$_2$Zn$_{20}$ is
close to a Kondo state with degeneracy $N$ = 2 and a much lower $T_K\sim$ 2 K.
Upon Co substitution, the coherence temperature of YbFe$_2$Zn$_{20}$ is
suppressed, accompanied by an emerging Schottky-like feature in specific heat
associated with the thermal depopulation of CEF levels upon cooling. For
0.4$\lesssim$ x $\lesssim$ 0.9, the ground state remains roughly the same which
can be qualitatively understood by Kondo effect in the presence of CEF
splitting. There is no clear indication of Kondo coherence observable in
resistivity within this substitution range down to 500 mK. The coherence
re-appears at around x$\gtrsim$ 0.9 and the coherence temperature increases
with higher Co concentration levels.
