Dirac/Weyl semimetals hosting linearly-dispersing bands have received recent attention for potential thermoelectric applications, since their ultrahigh-mobility carriers could generate large thermoelectric and Nernst power factors. To optimize these efficiencies, the Fermi energy needs to be chemically controlled in a wide range, which is generally difficult in bulk materials because of disorder effects from the substituted ions. Here it is shown that the Fermi energy is tunable across the Dirac point for layered magnet EuMnBi$_2$ by partially substituting Gd$^{3+}$ for Eu$^{2+}$ in the insulating block layer, which dopes electrons into the Dirac fermion layer without degrading the mobility. Clear quantum oscillation observed even in the doped samples allows us to quantitatively estimate the Fermi energy shift and optimize the power factor (exceeding 100 $mu$W/K$^2$cm at low temperatures) in combination with the first-principles calculation. Furthermore, it is shown that Nernst signal steeply increases with decreasing carrier density beyond a simple theoretical prediction, which likely originates from the field-induced gap reduction of the Dirac band due to the exchange interaction with the Eu moments. Thus, the magnetic block layer provides high controllability for the Dirac fermions in EuMnBi$_2$, which would make this series of materials an appealing platform for novel transport phenomena.
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