  In soft X-rays, the Monogem ring is an object with a diameter of 25{\deg}
located in the Galactic anti-centre. It is believed to be a faint, evolved,
local supernova remnant. The ring is also visible in the far-ultraviolet, and a
few optical filaments are related. It is not seen at radio wavelengths, as
other large supernova remnants are. We study a narrow about 4.5{\deg} long,
faint H$\alpha$-filament, G203.7+11.5,that is seen towards the centre of the
Monogem ring. It causes depolarisation and excessive Faraday rotation of radio
polarisation data. Polarisation observations at $\lambda$11\ cm and
$\lambda$21\ cm with the Effelsberg 100-m telescope were analysed. in addition
to $WMAP$ data, extragalactic rotation measures, and H$\alpha$ data. A
Faraday-screen model was applied. From the analysis of the depolarisation
properties of the H$\alpha$ filament, we derived a line-of-sight magnetic
field, $B_{||}$, of 26$\pm5\mu$G for a distance of 300~pc and an electron
density, $n_\mathrm{e}$, of 1.6~cm$^{-3}$. The absolute largest rotation
measure of G203.7+11.5 is -86$\pm3$~rad~ m$^{-2}$, where the magnetic field
direction has the opposite sign from the large-scale Galactic field. We
estimated the average synchrotron emissivity at $\lambda$21\ cm up to 300~pc
distance towards G203.7+11.5 to about 1.1~K $T_\mathrm{b}$/kpc, which is higher
than typical Milky Way values. The magnetic field within G203.7+11.5 is
unexpected in direction and strength. Most likely, the filament is related to
the Monogem-ring shock, where interactions with ambient clouds may cause local
magnetic field reversals. We confirm earlier findings of an enhanced but
direction-dependent local synchrotron emissivity.
