This paper reconstructs the cosmological background evolution under the scenario of dynamical dark energy using the Gaussian process approach, combining the latest Dark Energy Spectroscopic Instrument (DESI) baryon acoustic oscillations (BAO) data with other observations. The results reveal that the reconstructed dark-energy equation-of-state (EoS) parameter \( w(z) \) exhibits quintom-B behavior, crossing from the phantom to quintessence regime as the universe expands. The authors investigate this evolution from the perspectives of field theories and modified gravity, specifically \( f(R) \), \( f(T) \), and \( f(Q) \) theories. They show that certain modified gravity theories can exhibit quintom dynamics and fit the recent DESI data efficiently, with the quadratic deviation from the \(\Lambda\)CDM scenario being mildly favored. The paper also discusses the implications of this finding for the nature of dark energy and the \(\Lambda\)CDM paradigm, suggesting that modified gravity or other theoretical frameworks may provide alternative explanations for the observed dynamics.This paper reconstructs the cosmological background evolution under the scenario of dynamical dark energy using the Gaussian process approach, combining the latest Dark Energy Spectroscopic Instrument (DESI) baryon acoustic oscillations (BAO) data with other observations. The results reveal that the reconstructed dark-energy equation-of-state (EoS) parameter \( w(z) \) exhibits quintom-B behavior, crossing from the phantom to quintessence regime as the universe expands. The authors investigate this evolution from the perspectives of field theories and modified gravity, specifically \( f(R) \), \( f(T) \), and \( f(Q) \) theories. They show that certain modified gravity theories can exhibit quintom dynamics and fit the recent DESI data efficiently, with the quadratic deviation from the \(\Lambda\)CDM scenario being mildly favored. The paper also discusses the implications of this finding for the nature of dark energy and the \(\Lambda\)CDM paradigm, suggesting that modified gravity or other theoretical frameworks may provide alternative explanations for the observed dynamics.