  The accretion of matter onto intermediate polar White Dwarfs (IPWDs) seems to
provide attractive conditions for acceleration of particles to high energies in
a strongly magnetized turbulent region at the accretion disk inner radius. We
consider possible acceleration of electrons and hadrons in such region and
investigate their high energy radiation processes. It is concluded that
accelerated electrons loose energy mainly on synchrotron process producing
non-thermal X-ray emission. On the other hand, accelerated hadrons are
convected onto the WD surface and interact with dense matter. As a result, high
energy $\gamma$-rays from decay of neutral pions and secondary leptons from
decay of charged pions appear. We show that GeV-TeV $\gamma$-rays can escape
from the vicinity of the WD. Secondary leptons produce synchrotron radiation in
the hard X-rays and soft $\gamma$-rays. As an example, we predict the X-ray and
$\gamma$-ray emission from IPWD V1223 Sgr. Depending on the spectral index of
injected particles, this high energy emission may be detected by the ${\it
Fermi}$-LAT telescope and/or the future Cherenkov Telescope Array (CTA)
observatory.
