${\mathrm{GdFe}}_{2}{\mathrm{Zn}}_{20}$ is a complex cagelike compound with an unusually high ferromagnetic ordering temperature (${T}_{C}=86$ K) for a very diluted ${\mathrm{Gd}}^{3+}$ magnetic sublattice, embedded in a matrix that features strong electron-electron correlations. Here, we report on a magnetic and electronic study of the substitutional intermetallic system $\mathrm{Gd}{({\mathrm{Co}}_{1\ensuremath{-}y}{\mathrm{Fe}}_{y})}_{2}{\mathrm{Zn}}_{20}$ combining magnetization measurements plus first-principles density functional theory (DFT) calculations with temperature-dependent electron spin resonance (ESR). After accounting for electron-electron correlations and itinerant molecular field effects, the ESR results indicate that the exchange interaction between the ${\mathrm{Gd}}^{3+}$ is processed via a single band of $d$-type electrons at the Fermi level and the exchange interaction is covalent in nature $[J{(0)}_{fd}<0]$ with a strong conduction electron ($ce$) momentum transfer dependence $[{J}_{fd}(q)]$. The DFT calculations support this scenario by indicating a major contribution of $d$-type $ce$ at the Fermi level and a spin polarization in $(\text{Y},\mathrm{Gd}){\mathrm{Fe}}_{2}{\mathrm{Zn}}_{20}$ wherein the most stable configuration is antiferromagnetic between ${\mathrm{Gd}}^{3+}$ and $ce$ spins. Our results demonstrate that the standard Ruderman-Kittel-Kasuya-Yosida mechanism cannot explain the ferromagnetic behavior of ${\mathrm{GdFe}}_{2}{\mathrm{Zn}}_{20}$ and a superexchangelike mechanism is proposed for this magnetic interaction. An ``extended phase diagram'' for the double substitution sequence ${\mathrm{YCo}}_{2}{\mathrm{Zn}}_{20}\ensuremath{\rightarrow}{\mathrm{GdCo}}_{2}{\mathrm{Zn}}_{20}\ensuremath{\rightarrow}{\mathrm{GdFe}}_{2}{\mathrm{Zn}}_{20}$ is presented and discussed.