Left panel: 2D correlation of stellar distance vs. stellar metallicity. It is evident that metal-rich stars are predominantly located closer to the galactic center. This trend holds across all DM models, with a slight offset observed for ψDM. The data points are color-coded based on their stellar age, providing additional context. Right panel: 2D correlation of stellar spatial distribution vs. mean metallicity. The negative Spearman correlation coefficient indicates that older stars tend to be more metal-poor, while younger stars are more likely to be metal-rich. The data points are color-coded based on their mean stellar age, offering further insights. The vertical black line indicates the comoving limit, while the dashed line represents the ideal size of a core-halo structure.