A substantial body of astrophysical and astronomical evidence suggests that a significant portion of the mass/energy content of the Universe exists in the form of an exotic type of matter, the nature of which remains a mystery. This additional component, known as Dark Matter (DM), is estimated to make up about 24\% of the cosmic mass/energy content, outnumbering baryonic matter by a factor of five. Dark Matter is believed to consist of a new type of elementary particle that has eluded direct detection so far due to its extremely weak interaction with ordinary matter. The XENON Collaboration, dedicated to Dark Matter searches, has constructed an ultra-low background detector, the XENONnT detector, situated in the Laboratori Nazionali del Gran Sasso. This detector is designed to be sensitive to potential rare and low-energy interactions of DM particles with xenon atoms within its target. In this work, I concentrated on analyzing low-energy ionization signals related to interactions within the detector's active volume, seeking evidence of Dark Matter and, more broadly, Physics Beyond the Standard Model. In particular, to further lower the detector's threshold and enhance its sensitivity, I established a new model to accurately characterize the shape of ionization signals in the lowest possible energy regime, ranging from one to a few ionization electrons. To veto a substantial instrumental background that was caused by large ionization signals, I developed a framework to comprehensively capture the correlations among signals. This new analysis was initially tested on a small subset of the XENONnT Science Run 0 data during calibration, enabling us to establish competitive constraints on various physics beyond the Standard Model. In particular, we focused on three theoretical models: 1) the light Dark Matter, interacting with ordinary matter via electron scattering; 2) the dark photon, kinetically mixed with the Standard Model photons; and 3) the axion-like particles, coupling to the electrons. In the imminent future, we aim to apply it to the Science Run 0 official dataset, which is blinded at the moment, to enhance these constraints further and explore territories previously untouched. Finally, beyond the scope of the analysis of the ionization signal in XENONnT, I proposed a new mathematical method for revealing the time correlation between two populations in a dataset under the existence of both correlated and uncorrelated populations. This method provides a novel approach to modeling the time-correlated instrumental backgrounds and can potentially improve the detector sensitivity.