  The topological Hall effect (THE) and its thermoelectric counterpart, the
topological Nernst effect (TNE), are hallmarks of the skyrmion lattice phase
(SkL). We observed the giant TNE of the SkL in centrosymmetric Gd$_2$PdSi$_3$,
comparable in magnitude to the largest anomalous Nernst signals in
ferromagnets. Significant enhancement (suppression) of the THE occurs when
doping electrons (holes) to Gd$_2$PdSi$_3$. On the electron-doped side, the
topological Hall conductivity approaches the characteristic threshold $\sim
1000\,\left(\mathrm{\Omega cm}\right)^{-1}$ for the intrinsic regime. We use
the filling-controlled samples to confirm Mott's relation between TNE and THE
and discuss the importance of Gd-5d orbitals for transport in this compound.
