  The intrinsic antiferromagnetic topological insulator MnBi$_{2}$Te$_{4}$
undergoes a metamagnetic transition in a c-axis magnetic field. It has been
predicted that ferromagnetic MnBi$_{2}$Te$_{4}$ is an ideal Weyl semimetal with
a single pair of Weyl nodes. Here we report measurements of quantum
oscillations detected in the field-induced ferromagnetic phase of
MnBi$_{2-x}$Sb$_{x}$Te$_{4}$, where Sb substitution tunes the majority carriers
from electrons to holes. Single frequency Shubnikov-de Haas oscillations were
observed in a wide range of Sb concentrations (0.54 $\leq$ x $\leq$ 1.21). The
evolution of the oscillation frequency and the effective mass shows reasonable
agreement with the Weyl semimetal band-structure of ferromagnetic
MnBi$_{2}$Te$_{4}$ predicted by density functional calculations. Intriguingly,
the quantum oscillation frequency shows a strong temperature dependence,
indicating that the electronic structure sensitively depends on magnetism.
