XENON1T is a ton-scale liquid xenon time projection chamber primarily designed to search for dark matter. Due to its unprecedented low-background level, large detector mass, and low energy threshold, XENON1T is sensitive to a multitude of phenomena not described by the Standard Model (SM) of particle physics. In this work, XENON1T is used to search for electronic recoils induced by (1) solar axions, (2) a neutrino magnetic dipole moment, and (3) bosonic dark matter. To search for these signals, a full understanding of the detector response and sources of background is required. The event reconstruction and energy threshold are described in particular detail, and all known sources of background are characterized according to their energy spectra and temporal dependencies in order to develop a full background model predicting the energy spectrum of XENON1T electronic recoil data. When the XENON1T data is compared to this background prediction, an excess at low energies is observed that disfavors the background hypothesis at $\gtrsim 3\sigma$. A $\sim 6 \times 10^{-25}$ mol/mol concentration of tritium may explain the excess; however, such a small concentration is not possible to confirm independently. Without conclusive evidence of a new source of background, the excess is interpreted in the context of potential beyond-the-SM physics. A solar axion model with axion-electron coupling $g_{ae} \sim 3\times10^{-12}$, favored at 3.4$\sigma$, describes the observed excess the best, followed by an enhanced neutrino magnetic moment $\mu_{\nu} \sim 2\times10^{-11}~\mu_B$ (3.2$\sigma$), and a 2.3 keV bosonic dark matter particle (3.0$\sigma$, global). If the excess persists, XENONnT, the successor to XENON1T, will be able to determine its origins likely within a few months of science data.



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