  We report results of our low-temperature magneto electric transport
measurements on micron-sized short cylinders of odd-parity, spin-triplet
superconductor Sr$_2$RuO$_4$ with the cylinder axis along the $c$ axis. The
in-plane magnetic field and measurement current dependent magnetoresistance
oscillations were found to feature an amplitude much larger than that expected
from the conventional Little-Parks effect, suggesting that the
magnetoresistance oscillations originate from vortex crossing. The free-energy
barrier that controls the vortex crossing was modulated by the magnetic flux
enclosed in the cylinder, the in-plane field, measurement current, and
structural factors. Distinct features on magnetoresistance peaks were found,
which we argue to be related to the emergence of half-flux quantum states, but
only in samples for which the vortex crossing is confined at specific parts of
the sample.
