  We present the study on the X-ray emission for a sample of radio-detected
quasars constructed from the cross-matches between SDSS, FIRST catalogs and
XMM-Newton archives. A sample of radio-quiet SDSS quasars without FIRST radio
detection is also assembled for comparison. We construct the optical and X-ray
composite spectra normalized at rest frame $4215\,\rm \AA$ (or $2200\,\rm \AA$)
for both radio-loud quasars (RLQs) and radio-quiet quasars (RQQs) at $z\le3.2$,
with matched X-ray completeness of 19\%, redshift and optical luminosity. While
the optical composite spectrum of RLQs is similar to that of RQQs, we find that
RLQs have higher X-ray composite spectrum than RQQs, consistent with previous
studies in the literature. By dividing the radio-detected quasars into radio
loudness bins, we find the X-ray composite spectra are generally higher with
increasing radio loudness. Moreover, a significant correlation is found between
the optical-to-X-ray spectral index and radio loudness, and there is a unified
multi-correlation between the radio, X-ray luminosities and radio loudness in
radio-detected quasars. These results could be possibly explained with the
corona-jet model, in which the corona and jet are directly related.
