The cataclysmic variable (CV) is a binary system composed of a white-dwarf (WD) primary and a low-mass main-sequence star. The accretion onto the WD surface causes an X-ray emission, and the CVs are one of the major Galactic X-ray sources. The eROSITA observation offers a new opportunity to identify numerous X-ray-emitting CVs and advance our understanding of its Galactic population. We aim to search for candidates of the X-ray-emitting CVs in the four catalogs of eROSITA, XMM-Newton, Swift, and ROSAT observations. We also intend to examine how the eROSITA survey can enhance the search for new X-ray-emitting CVs. In this study, we identified the candidates of the X-ray-emitting CVs by cross-matching among the four X-ray catalogs and the Gaia sources that are selected from the bridge region between the main sequence and the WD's cooling sequence in the Hertzsprung-Russell diagram. For the selected candidates, we searched for the periodic modulation in the photometry light curves taken by the ZTF and/or TESS observations. The cross-matching selects 444 candidates of the X-ray-emitting CVs, in which 267 sources are the identified CVs. In the other 177 candidates of the X-ray-emitting CVs, we identify possible orbital modulation for 56 sources in ZTF/TESS light curves. About 51% of the candidates are exclusively selected from the eROSITA catalog, while about 36%, 9%, and 4% are selected from the XMM-Newton, Swift, and ROSAT catalogs, respectively. In the color-color diagram, most of the selected CV candidates are distinguished from the active stars, while some sources are likely classified as eclipsing binary systems rather than CVs. Combining the cross-matching process between X-ray catalogs and Gaia sources with the timing analysis of the ZTF/TESS data is an effective tool to identify the candidates of X-ray-emitting CVs. In particular, the eROSITA observation successfully identified the sources that have been missed in the other three catalogs because of its wide coverage on the sky region and high flux sensitivity. On the other hand, the current flux sensitivity of eROSITA is limited to on the order of ~10^-14^erg/cm^-2^/s. As the first eROSITA catalog is result of the operation in the first six months, it is expected that the future operation will further increase the population of known X-ray-emitting CVs.