This study explores the Garcia-Salcedo ghost dark energy (GDE) and generalized ghost dark energy (GGDE) models within the context of the $f(\mathrm{R}, \mathrm{T}^2)$ theory, where $\mathrm{R}$ is the Ricci scalar and $\mathrm{T}^2$ is the self-contraction of the stress-energy tensor. The focus is on the non-interacting case in a flat Friedmann-Robertson-Walker (FRW) universe. The authors reconstruct $f(\mathrm{R}, \mathrm{T}^2)$ gravity models using the GDE and GGDE models and analyze their evolutionary behavior and stability. The behavior of the equation of state (EoS) parameter is also examined. The results show that some of the reconstructed $f(\mathrm{R}, \mathrm{T}^2)$ models successfully describe both the phantom and quintessence epochs of the universe, supporting the current cosmic accelerated expansion. The study reveals intricate connections between dark energy models and modified gravitational theories, providing significant insights into the dynamics of the cosmos on a large scale. The paper concludes with a discussion of the implications of these findings for understanding cosmic evolution and the nature of dark energy.This study explores the Garcia-Salcedo ghost dark energy (GDE) and generalized ghost dark energy (GGDE) models within the context of the $f(\mathrm{R}, \mathrm{T}^2)$ theory, where $\mathrm{R}$ is the Ricci scalar and $\mathrm{T}^2$ is the self-contraction of the stress-energy tensor. The focus is on the non-interacting case in a flat Friedmann-Robertson-Walker (FRW) universe. The authors reconstruct $f(\mathrm{R}, \mathrm{T}^2)$ gravity models using the GDE and GGDE models and analyze their evolutionary behavior and stability. The behavior of the equation of state (EoS) parameter is also examined. The results show that some of the reconstructed $f(\mathrm{R}, \mathrm{T}^2)$ models successfully describe both the phantom and quintessence epochs of the universe, supporting the current cosmic accelerated expansion. The study reveals intricate connections between dark energy models and modified gravitational theories, providing significant insights into the dynamics of the cosmos on a large scale. The paper concludes with a discussion of the implications of these findings for understanding cosmic evolution and the nature of dark energy.