  Results are presented for a semi-coherent search for continuous gravitational
waves from the millisecond pulsar PSR J0437$-$4715, using a hidden Markov model
to track spin wandering, in LIGO data from the third LIGO-Virgo observing run.
This is the first search for PSR J0437$-$4715 to cover a wide frequency range
from $60$ Hz to $500$ Hz and simultanously accommodate random spin deviations
from the secular radio ephemeris. Two searches are performed with plausible
coherence times of $10$ days and $30$ days, as the frequency wandering
time-scale of the gravitational-wave-emitting quadrupole is unknown. The former
analysis yields no surviving candidates, while the latter yields five
candidates after the veto procedure. The detection statistic of each of the
five survivors is mapped as a function of sky position, in preparation for
follow-up analyses in the future, e.g. during LIGO-Virgo-KAGRA fourth observing
run.
