  We report X-ray observations of the newly discovered pulsating white dwarf
eRASSU J191213.9-441044 with Spectrum Roentgen Gamma and eROSITA (SRG/eROSITA)
and XMM-Newton. The new source was discovered during the first eROSITA all-sky
survey at a flux level of fX (0.2 - 2.3 keV) = 3.3 e-13 erg cm-2 s-1 and found
to be spatially coincident with a G = 17.1 stellar Gaia-source at a distance of
237 pc. The flux dropped to about fX = 1 e-13 erg cm-2 s-1 during the three
following eROSITA all-sky surveys and remained at this lower level during
dedicated XMM-Newton observations performed in September 2022. With XMM-Newton,
pulsations with a period of 319 s were found at X-ray and ultraviolet
wavelengths occurring simultaneously in time, thus confirming the nature of
eRASSU J191213.9-441044 as the second white-dwarf pulsar. The X-ray and
UV-pulses correspond to broad optical pulses. Narrow optical pulses that
occurred occasionally during simultaneous XMM-Newton/ULTRACAM observations have
no X-ray counterpart. The orbital variability of the X-ray signal with a
roughly sinusoidal shape was observed with a pulsed fraction of ~28% and
maximum emission at orbital phase ~0.25. The ultraviolet light curve peaks at
around binary phase 0.45. The X-ray spectrum can be described with the sum of a
power law spectrum and a thermal component with a mean X-ray luminosity of
Lx(0.2-10 keV) = 1.4 e30 erg s-1. The spectral and variability properties could
indicate some residual accretion, in contrast to the case of the prototypical
object AR Sco.
