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Context. To explain the well-known tension between cosmological parameter constraints obtained from the primary cosmic microwave background (CMB) and those drawn from X-ray-selected galaxy cluster samples identified with early data, we propose a possible explanation for the incompleteness of detected clusters being higher than estimated. Specifically, we suggest that certain types of galaxy groups or clusters may have been overlooked in previous works. Aims. We aim to search for galaxy groups and clusters with especially extended surface brightness distributions by creating a new X-ray-selected catalog of extended galaxy clusters from the XMM-SpitzerExtragalactic Representative Volume Survey (XMM-SERVS) data, based on a dedicated source detection and characterization algorithm optimized for extended sources. Methods. Our state-of-the-art algorithm is composed of wavelet filtering, source detection, and characterization. We carried out a visual inspection of the optical image, and spatial distribution of galaxies within the same redshift layer to confirm the existence of clusters and estimated the cluster redshift with the spectroscopic and photometric redshifts of galaxies. The growth curve analysis was used to characterize the detections. Results. We present a catalog of extended X-ray galaxy clusters detected from the XMM-SERVS data. The XMM-SERVS X-ray eXtended Galaxy Cluster (XVXGC) catalog features 141 cluster candidates. Specifically, there are 53 clusters previously identified as clusters with intracluster medium (ICM) emission (class 3); 40 that were previously known as optical or infrared (IR) clusters, but detected as X-ray clusters for the first time (class 2); and 48 identified as clusters for the first time (class 1). Compared with the class 3 sample, the “class 1 + class 2” sample is systematically fainter and exhibits a flatter surface brightness profile. Specifically, the median flux in [0.5–2.0] keV band for “class 1 + class 2” and class 3 sample is 1.288 × 10⁻¹⁴erg/s/cm²and 1.887 × 10⁻¹⁴erg/s/cm², respectively. The median values ofβ(i.e., the slope of the cluster surface brightness profile) are 0.506 and 0.573 for the “class 1 + class 2” and class 3 samples, respectively. The entire sample is available at the CDS.