A recent study showed that, in spin-1 chiral fermion systems composed of two linearly dispersing bands and one trivial band, impurity scattering produces an asymmetric cusp in the spectral conductivity σ(ϵ). We demonstrate that this asymmetric cusp markedly enhances the electronic thermoelectric response. Using linear-response theory within the self-consistent Born approximation, we find low-temperature enhancements in both the Seebeck coefficient and the electronic figure of merit. Increasing the curvature of the trivial band further strengthens this cusp-induced enhancement, even though the corresponding density of states becomes smoother. To clarify this mechanism, we introduce a minimal cusp model for σ(ϵ) and show that the enhancement is most pronounced when the cusp is sharp and strongly asymmetric, and when the spectral conductivity at the cusp energy is small.