This paper presents a cosmological analysis of exponential quintessence with non-zero spatial curvature, motivated by string theory. The model is tested against recent cosmological data including Planck CMB, DESI BAO, and supernovae datasets. The potential is given by $ V = V_0 e^{-\lambda \phi} $, and the analysis includes both open and closed universes. The results show a preference for non-zero values of $ \lambda $, with $ \lambda = 0.48_{-0.21}^{+0.28} $, $ 0.68_{-0.20}^{+0.31} $, and $ 0.77_{-0.15}^{+0.18} $ at 68% confidence level. No significant hint for spatial curvature is found. The analysis also shows that the model's parameters are consistent with the standard $ \Lambda $CDM model, but with a slight preference for a non-zero $ \lambda $. The results indicate that the universe may evolve towards an eternally accelerating fixed point, suggesting the presence of a cosmological horizon. The study also compares the model with the $ w_0w_a $ parametrization and finds a mild preference for the latter. The results highlight the importance of considering spatial curvature in dark energy models and the need for further studies to better understand the nature of dark energy.This paper presents a cosmological analysis of exponential quintessence with non-zero spatial curvature, motivated by string theory. The model is tested against recent cosmological data including Planck CMB, DESI BAO, and supernovae datasets. The potential is given by $ V = V_0 e^{-\lambda \phi} $, and the analysis includes both open and closed universes. The results show a preference for non-zero values of $ \lambda $, with $ \lambda = 0.48_{-0.21}^{+0.28} $, $ 0.68_{-0.20}^{+0.31} $, and $ 0.77_{-0.15}^{+0.18} $ at 68% confidence level. No significant hint for spatial curvature is found. The analysis also shows that the model's parameters are consistent with the standard $ \Lambda $CDM model, but with a slight preference for a non-zero $ \lambda $. The results indicate that the universe may evolve towards an eternally accelerating fixed point, suggesting the presence of a cosmological horizon. The study also compares the model with the $ w_0w_a $ parametrization and finds a mild preference for the latter. The results highlight the importance of considering spatial curvature in dark energy models and the need for further studies to better understand the nature of dark energy.