  We observed 51 sources in the Q-U-I JOint TEnerife (QUIJOTE) cosmological
fields which were brighter than 1 Jy at 30 GHz in the Planck Point Source
Catalogue (version 1), with the Very Large Array at 28 -- 40 GHz, in order to
characterise their high-radio-frequency variability and polarization
properties. We find a roughly log-normal distribution of polarization fractions
with a median of 2%, in agreement with previous studies, and a median rotation
measure (RM) of $\approx$ 1110 rad m$^{-2}$ with one outlier up to $\approx$
64000 rad m$^{-2}$ which is among the highest RMs measured in quasar cores. We
find hints of a correlation between the total intensity flux density and median
polarization fraction. We find 59% of sources are variable in total intensity,
and 100% in polarization at $3\sigma$ level, with no apparent correlation
between total intensity variability and polarization variability. This
indicates that it will be difficult to model these sources without simultaneous
polarimetric monitoring observations and they will need to be masked for
cosmological analysis.
