  Magnets, with topologically-nontrivial Dirac/Weyl points, have recently
attracted significant attention owing to the unconventional physical
properties, such as large anomalous Hall effects. However, they typically have
a high carrier density and complicated band structure near the Fermi energy. In
this study, we report degenerate magnetic semiconductor EuMg$_2$Bi$_2$, which
exhibits a single valley at the $\Gamma$ point, where the field-tunable Weyl
points form via the magnetic exchange interaction with the local Eu spins. By
the high-field measurements on high-quality single crystals, we observed the
quantum oscillations in resistivity, elastic constant, and surface impedance,
which enabled us to determine the position of the Fermi energy. In combination
with the first-principles calculation, we revealed that the Weyl points are
located in the vicinity of the Fermi energy when the Eu spins are fully
polarized. Furthermore, we observed large anomalous Hall effect (Hall angle
$\Theta_{\mathrm{AH}}\sim0.07$) in the forced ferromagnetic phase, which is
consistent with this field variation of band structure.
