This paper presents a study on quintom cosmology and modified gravity using the latest DESI baryon acoustic oscillation (BAO) data. The authors reconstruct the dark energy equation of state (EoS) parameter $ w(z) $ using a Gaussian process approach, revealing a quintom-B behavior, where dark energy transitions from the phantom regime to the quintessence regime as the universe expands. This behavior is consistent with the observed data and challenges the standard $ \Lambda $ CDM model. The study investigates whether this behavior can be explained by modified gravity theories, specifically $ f(R) $, $ f(T) $, and $ f(Q) $ gravity. The results show that these modified gravity models can reproduce the observed dark energy dynamics and provide a quadratic deviation from the $ \Lambda $ CDM scenario, which is mildly favored by the data. The study also highlights the importance of observational data in constraining dark energy models and the potential of modified gravity theories to explain the observed dynamics of dark energy. The results suggest that the inclusion of DESI data shifts the redshift at which dark energy crosses the phantom divide to higher values, indicating a more complex evolution of dark energy. The study concludes that modified gravity theories can provide a viable explanation for the observed dynamics of dark energy, offering a promising avenue for further research in cosmology.This paper presents a study on quintom cosmology and modified gravity using the latest DESI baryon acoustic oscillation (BAO) data. The authors reconstruct the dark energy equation of state (EoS) parameter $ w(z) $ using a Gaussian process approach, revealing a quintom-B behavior, where dark energy transitions from the phantom regime to the quintessence regime as the universe expands. This behavior is consistent with the observed data and challenges the standard $ \Lambda $ CDM model. The study investigates whether this behavior can be explained by modified gravity theories, specifically $ f(R) $, $ f(T) $, and $ f(Q) $ gravity. The results show that these modified gravity models can reproduce the observed dark energy dynamics and provide a quadratic deviation from the $ \Lambda $ CDM scenario, which is mildly favored by the data. The study also highlights the importance of observational data in constraining dark energy models and the potential of modified gravity theories to explain the observed dynamics of dark energy. The results suggest that the inclusion of DESI data shifts the redshift at which dark energy crosses the phantom divide to higher values, indicating a more complex evolution of dark energy. The study concludes that modified gravity theories can provide a viable explanation for the observed dynamics of dark energy, offering a promising avenue for further research in cosmology.