The presence of the apparently extended hard (2-10keV) X-ray emission along the Galactic plane has been known since the early 1980s. With a deep X-ray exposure using the Chandra X-ray Observatory of a slightly off-plane region in the Galactic bulge, most of the extended emission was resolved into faint discrete X-ray sources in the Fe K band (Revnivtsev et al., 2009Natur.458.1142R). The major constituents of these sources have long been considered to be X-ray active stars and magnetic cataclysmic variables (CVs). However, recent works including our near-infrared (NIR) imaging and spectroscopic studies (Morihana et al., 2013ApJ...766...14M, Cat. J/ApJ/766/14; Morihana et al., 2016PASJ...68...57M) argue that other populations should be more dominant. To investigate this further, we conducted a much deeper NIR imaging observation at the center of the Chandra's exposure field. We have used the MOIRCS on the Subaru telescope, reaching the limiting magnitude of ~18mag in the J, H, and K_s_ bands in this crowded region, and identified ~50% of the X-ray sources with NIR candidate counterparts. We classified the X-ray sources into three groups (A, B, and C) based on their positions in the X-ray color-color diagram and characterized them based on the X-ray and NIR features. We argue that the major populations of the Group A and C sources are, respectively, CVs (binaries containing magnetic or non-magnetic white dwarfs with high accretion rates) and X-ray active stars. The major population of the Group B sources is presumably white dwarf (WD) binaries with low mass accretion rates. The Fe K equivalent width in the composite X-ray spectrum of the Group B sources is the largest among the three and comparable to that of the Galactic bulge X-ray emission. This leads us to speculate that there are numerous WD binaries with low mass accretion rates which are not recognized as CVs but are the major contributor of the apparently extended X-ray emission.