  We report our high-resolution (0.03 arcsec to 0.07 arcsec) ALMA imaging of
the quadruply lensed radio-loud quasar MG\,J0414+0534 at redshift $z=2.639$ in
the continuum and the broad CO(11-10) line at $\sim 340\,$GHz. With the help of
strong lensing magnification and ALMA's high-resolution, we succeeded in
resolving the jet/dust and CO gas in the quasar host galaxy both extending up
to $\sim 1\,$kpc, with a resolution of $\sim 50\,$pc for the first time. Both
the continuum emission and the CO(11-10) line have a similar bimodal structure
aligned with the quasar jets ($\sim 200\,$pc) observed by Very Long Baseline
Interferometry (VLBI) at $5\,$GHz and $8.4\,$GHz. The CO gas in the vicinity of
both the eastern and western jet components at the location of $\sim 80\,$pc
from the quasar core are moving at high velocities up to $\pm
600\,$$\textrm{km}\,\textrm{s}^{-1}$ relative to the core. The observed
features show clear evidence of strong interaction between the jets and
interstellar medium (ISM). High temperature and high density environments in
the ISM of the quasar host galaxy, as suggested from CO line ratios, also
support this result. The small scale of the jets, the jet-ISM interaction, and
the continuum spectral energy distribution of this source indicate that we are
watching the infancy stage of quasar radio activity.
