  We describe a synthetic three-leg Hall ladder system with a tunable magnetic
flux for neutral $^{173}$Yb atoms in a one-dimensional optical lattice. The
ladder legs are formed by three hyperfine ground spin states of the atoms, and
the complex interleg links are generated through Raman couplings between the
spin states using multiple laser beams. The effective magnetic flux through a
ladder plaquette, $\phi$, is controlled by the angles of the Raman laser beams
with the lattice axis. We investigate the quench dynamics of the Hall ladder
system for $\phi\approx\frac{\pi}{3}, \frac{\pi}{2},$ and $\frac{2\pi}{3}$
after a sudden application of the Raman coupling in various interleg link
configurations. The semi-classical trajectory of the atoms in the plane of the
spin composition and lattice position exhibits the characteristic motion for
the effective magnetic field. In a tube configuration with the three legs
cyclically linked, the quench evolution was observed to be substantially
damped, which is attributed to the random flux threading the Hall tube.
