  We use high resolution hydrodynamical simulations to study the contribution
to the X-ray background from high-$z$ energetic sources, such as X-ray
binaries, accreting nuclear black holes and shock heated interstellar medium.
Adopting the model discussed in Eide et al. (2018), we find that these X-ray
sources during the Epoch of Reionization (EoR) contribute less than a few
percent of the unresolved X-ray background. The same sources contribute to less
than $\sim$2\% of the measured angular power spectrum of the fluctuations of
the X-ray background. The outputs of radiative transfer simulations modeling
the EoR are used to evaluate the cross-correlations of X-ray background with
the 21~cm signal from neutral hydrogen. Such correlation could be used to
confirm the origin of the 21 cm signal, as well as give information on the
properties of the X-ray sources during the EoR. We find that the correlations
are positive during the early stages of reionization when most of the hydrogen
is neutral, while they become negative when the intergalactic medium gets
highly ionized, with the transition from positive to negative depending on both
the X-ray model and the scale under consideration. With {\tt SKA} as the
reference instrument for the 21~cm experiment, the predicted S/N for such
correlations is $<1$ if the corresponding X-ray survey is only able to resolve
and remove X-ray sources with observed flux $>10^{-15}\,\rm erg\, cm^{-2} \,
s^{-1}$, while the cumulative S/N from $l=1000$ to $10^{4}$ at $x_{\rm HI}=0.5$
is $\sim 5$ if sources with observed flux $>10^{-17}\,\rm erg\, cm^{-2} \,
s^{-1}$ are detected.
