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 $zle3.2$, 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.
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