  To explain the well-known tension between cosmological parameter constraints
obtained from the primary CMB and those drawn from galaxy cluster samples, we
propose a possible explanation for the incompleteness of detected clusters are
higher than estimated. We aim to search for galaxy groups and clusters with
particularly extended surface brightness distributions by creating a new
X-ray-selected catalog of extended galaxy clusters from the XMM-SERVS data,
based on a dedicated source detection and characterization algorithm that is
optimized for extended sources. Our state-of-the-art algorithm is composed of
wavelet filtering, source detection, and characterization. We make a visual
inspection of the optical image, and spatial distribution of galaxies within
the same redshift layer to confirm the existence of clusters and estimate the
cluster redshift with the spectroscopic and photometric redshifts of galaxies.
The growth curve analysis is used to characterize the detections. We report a
catalog of extended X-ray galaxy clusters detected from the XMM-SERVS data,
named the XMM- SERVS X-ray eXtended Galaxy Cluster (XVXGC) catalog. It includes
141 cluster candidates. Specifically, there are 52 clusters previously
identified as clusters with the intra-cluster medium (ICM) emission (class 3),
37 ones previously known as optical or infrared clusters but detected as X-ray
clusters for the first time (class 2), and 52 identified as clusters for the
first time (class 1). Compared with the class3 sample, the 'class1+2' sample is
systematically fainter, and exhibits a flatter surface brightness profile. The
median flux in [0.1-2.4]keV band for 'class1+2' and class3 sample is 2.336e-14
and 3.163e-14erg/s/cm2, respectively. The median slope of surface brightness
profile are 0.502 and 0.577 for the 'class1+2' and class 3 samples,
respectively.
