  We report a study of isoelectronic chemical substitution in the recently
discovered quantum critical ferromagnet CeRh$_6$Ge$_4$. Upon silicon-doping,
the ferromagnetic ordering temperature of CeRh$_6$(Ge$_{1-x}$Si$_x$)$_4$ is
continuously suppressed, and no transition is observed beyond
$x_c$$\approx$0.125. Non-Fermi liquid behavior with $C/T \propto$log($T^*/T$)
is observed close to $x_c$, indicating the existence of strong quantum
fluctuations, while the $T$-linear behavior observed upon pressurizing the
parent compound is absent in the resistivity, which appears to be a consequence
of the disorder induced by silicon doping. Our findings provide evidence for
the role played by disorder on the unusual ferromagnetic quantum criticality in
CeRh$_6$Ge$_4$, and provides further evidence for understanding the origin of
this behavior.
