ABSTRACT With an aim to unveil the population of obscured active galactic nuclei (AGN) hosted in high-z dust-obscured galaxies (DOGs), we performed X-ray spectral study of 34 DOGs (0.59 ≤ z ≤ 4.65) lying within 5.3 square degrees of the XMM-Spitzer Extragalactic Representative Volume Survey (XMM-SERVS) coverage in the XMM-Large Scale Structure (XMM-LSS) field. To improve the spectral quality of individual sources, we combined all the existing XMM−Newton data and also included Chandra/Advanced CCD Imaging Spectrometer (ACIS) data, whenever available. We find that the X-ray spectra of our DOGs can be fitted with a simple absorbed power law or with a physically motivated borus02 model. The line-of-sight column densities (NH) in our sources span across a wide range (1.02 × 1022 cm−2 ≤ NH ≤ 1.21 × 1024 cm−2), with a substantial fraction (∼17.6 per cent) of them being heavily obscured (NH ≥ 1023 cm−2). We also identified one new Compton-thick (CT)-AGN candidate, yielding the CT-AGN fraction in our sample to be only 3 per cent. The absorption-corrected 2.0–10 keV X-ray luminosities of our sources (2.00 × 1043 erg s−1 ≤ $L_{\rm 2-10~keV}^{\rm int}$ ≤ 6.17 × 1045 erg s−1) suggest them to be luminous quasars. The NH versus Eddington ratio diagnostic plot infers that our sample consists of a heterogeneous population that includes a small fraction (∼12 per cent) of DOGs belonging to an early phase (Hot DOGs) during which accretion and obscuration peaks, while the remaining DOGs belong to an intermediate or late phase during which radiative feedback from the dominant AGN blows away surrounding obscuring material.