This study explores the Garcia-Salcedo ghost dark energy (GDE) and generalized ghost dark energy (GGDE) models within the framework of $ f(R, T^2) $ gravity theory, where $ R $ is the Ricci scalar and $ T^2 $ is the self-contraction of the stress-energy tensor. The research focuses on the non-interacting case in a flat Friedmann-Robertson-Walker (FRW) universe. The $ f(R, T^2) $ gravity models are reconstructed using these dark energy models, and the stability and behavior of the equation of state (EoS) parameter are analyzed. The results show that some reconstructed $ f(R, T^2) $ models effectively describe both the phantom and quintessence epochs of the universe, supporting the current cosmic accelerated expansion. The study reveals the complex interplay between dark energy models and modified gravitational theories, offering insights into the large-scale dynamics of the cosmos. The Garcia-Salcedo GDE model incorporates ghost fields inspired by quantum chromodynamics (QCD), providing a novel perspective on dark energy. The EoS parameter for this model is found to be greater than -1, indicating a quintessence era, consistent with observational data. However, the reconstructed $ f(R, T^2) $ model based on this model is found to be unstable under linear perturbations. The GGDE model, defined by the Veneziano ghost field, is also analyzed. The EoS parameter for this model is found to be less than -1, indicating a phantom era, which is not viable under recent observational data. The reconstructed $ f(R, T^2) $ model based on the GGDE model is also found to be unstable. The study also examines the $ f(R, T^2) = f_1(R) + f_2(T^2) $ gravity model, which combines different functional forms of $ R $ and $ T^2 $. The reconstructed model shows monotonically increasing behavior, consistent with the phantom era. However, the null energy condition (NEC) is violated, indicating the presence of exotic matter, which is not viable under recent observational data. Overall, the study highlights the importance of understanding the dynamics of dark energy and modified gravity theories in explaining cosmic acceleration and the evolution of the universe. The findings suggest that while some models show promise in describing cosmic phenomena, others are not viable due to instability or violation of fundamental physical conditions. The research contributes to the broader understanding of dark energy and modified gravity theories in the context of cosmic evolution.This study explores the Garcia-Salcedo ghost dark energy (GDE) and generalized ghost dark energy (GGDE) models within the framework of $ f(R, T^2) $ gravity theory, where $ R $ is the Ricci scalar and $ T^2 $ is the self-contraction of the stress-energy tensor. The research focuses on the non-interacting case in a flat Friedmann-Robertson-Walker (FRW) universe. The $ f(R, T^2) $ gravity models are reconstructed using these dark energy models, and the stability and behavior of the equation of state (EoS) parameter are analyzed. The results show that some reconstructed $ f(R, T^2) $ models effectively describe both the phantom and quintessence epochs of the universe, supporting the current cosmic accelerated expansion. The study reveals the complex interplay between dark energy models and modified gravitational theories, offering insights into the large-scale dynamics of the cosmos. The Garcia-Salcedo GDE model incorporates ghost fields inspired by quantum chromodynamics (QCD), providing a novel perspective on dark energy. The EoS parameter for this model is found to be greater than -1, indicating a quintessence era, consistent with observational data. However, the reconstructed $ f(R, T^2) $ model based on this model is found to be unstable under linear perturbations. The GGDE model, defined by the Veneziano ghost field, is also analyzed. The EoS parameter for this model is found to be less than -1, indicating a phantom era, which is not viable under recent observational data. The reconstructed $ f(R, T^2) $ model based on the GGDE model is also found to be unstable. The study also examines the $ f(R, T^2) = f_1(R) + f_2(T^2) $ gravity model, which combines different functional forms of $ R $ and $ T^2 $. The reconstructed model shows monotonically increasing behavior, consistent with the phantom era. However, the null energy condition (NEC) is violated, indicating the presence of exotic matter, which is not viable under recent observational data. Overall, the study highlights the importance of understanding the dynamics of dark energy and modified gravity theories in explaining cosmic acceleration and the evolution of the universe. The findings suggest that while some models show promise in describing cosmic phenomena, others are not viable due to instability or violation of fundamental physical conditions. The research contributes to the broader understanding of dark energy and modified gravity theories in the context of cosmic evolution.