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Numerous studies of integrated starlight, stellar counts, and kinematics haveconfirmed that the Milky Way is a barred galaxy. However, far fewer studieshave investigated the bar's stellar population properties, which carry valuableindependent information regarding the bar's formation history. Here we conducta detailed analysis of chemical abundance distributions ([Fe/H] and [Mg/Fe]) inthe on-bar and off-bar regions to study the azimuthal variation of starformation history (SFH) in the inner Galaxy. We find that the on-bar andoff-bar stars at Galactocentric radii 3 $< r_{\rm GC}<$ 5 kpc have remarkablyconsistent [Fe/H] and [Mg/Fe] distribution functions and [Mg/Fe]--[Fe/H]relation, suggesting a common SFH shared by the long bar and the disc. Incontrast, the bar and disc at smaller radii (2 $< r_{\rm GC} <$ 3 kpc) shownoticeable differences, with relatively more very metal-rich ([Fe/H]~0.4) starsbut fewer solar abundance stars in the bar. Given the three-phase starformation history proposed for the inner Galaxy in Lian et al. (2020b), thesedifferences could be explained by the off-bar disc having experienced either afaster early quenching process or recent metal-poor gas accretion. Verticalvariations of the abundance distributions at small $r_{\rm GC}$ suggest a widervertical distribution of low-$\alpha$ stars in the bar, which may serve aschemical evidence for vertical heating through the bar buckling process. Thelack of such vertical variations outside the bulge may then suggest a lack ofvertical heating in the long bar.

The chemical properties of the Milky Way's on-bar and off-bar regions: evidence for inhomogeneous star formation history in the bulge