We conducted an extensive identification and analysis of various morphological classes and subclasses of radio galaxies using the latest high-resolution data from the second data release of the LOFAR Two-metre Sky Survey. This paper presents the first results of our large-scale investigation: a new catalog of "winged" radio galaxies (WRGs). These objects represent a fascinating class of irregular radio galaxies, characterized by a pair of secondary radio lobes ("wings") in addition to the primary active lobes. We identified and cataloged 621 new WRGs and 403 additional candidates. Among the confirmed winged sources, 382 are classified as "X"-shaped radio galaxies, while the remaining 239 are "Z"-shaped radio galaxies. We also estimated several basic parameters for these winged sources and performed a Fanaroff-Riley classification. Our results show that the majority of the sources (~88%) exhibit edge- brightened radio lobes and high average radio power (log_10_[P_144MHz_WHz^-1^]=26.25), consistent with an FR II classification. The average spectral index between 144MHz and 1.4GHz is -0.84, which is steeper than that found for previously identified winged sources based on higher-frequency data from the Very Large Array Faint Images of the Radio Sky at Twenty-centimeters survey. This indicates that our study is capable of detecting fainter sources. The median linear size of the winged sources, 498kpc, confirms that these are large-scale structures, with approximately 16% having sizes exceeding 0.7Mpc, making them potential candidates for giant radio galaxies.