  Results are presented for a semi-coherent search for continuous gravitational
waves from the low-mass X-ray binary Scorpius X-1, using a hidden Markov model
(HMM) to allow for spin wandering. This search improves on previous HMM-based
searches of Laser Interferometer Gravitational-wave Observatory (LIGO) data by
including the orbital period in the search template grid, and by analyzing data
from the latest (third) observing run (O3). In the frequency range searched,
from 60 to 500 Hz, we find no evidence of gravitational radiation. This is the
most sensitive search for Scorpius X-1 using a HMM to date. For the most
sensitive sub-band, starting at $256.06$Hz, we report an upper limit on
gravitational wave strain (at $95 \%$ confidence) of
$h_{0}^{95\%}=6.16\times10^{-26}$, assuming the orbital inclination angle takes
its electromagnetically restricted value $\iota=44^{\circ}$. The upper limits
on gravitational wave strain reported here are on average a factor of $\sim 3$
lower than in the O2 HMM search. This is the first Scorpius X-1 HMM search with
upper limits that reach below the indirect torque-balance limit for certain
sub-bands, assuming $\iota=44^{\circ}$.
