We report the detection of a large sample of high-$alpha$-metal-rich stars on the low giant branch with $2.6<logg<3.3$ dex in the LAMOST-MRS survey. This special group corresponds to an intermediate-age population of $5-9$ Gyr based on the $[Fe/H]$-$[C/N]$ diagram and age-$[C/N]$ calibration. A comparison group is selected to have solar $alpha$ ratio at super metallicity, which is young and has a narrow age range around 3 Gyr. Both groups have thin-disk like kinematics but the former shows slightly large velocity dispersions. The special group shows a larger extension in vertical distance toward 1.2 kpc, a second peak at smaller Galactic radius and a larger fraction of super metal rich stars with $[Fe/H]>0.2$ than the comparison group. These properties strongly indicate its connection with the outer bar/bulge region at $R=3-5$ kpc. A tentative interpretation of this special group is that its stars were formed in the X-shaped bar/bulge region, close to its corotation radius, where radial migration is the most intense, and brings them to present locations at 9 kpc and beyond. Low eccentricities and slightly outward radial excursions of its stars are consistent with this scenario. Its kinematics (cold) and chemistry ($[alpha/Fe]$ $sim 0.1$) further support the formation of the instability-driven X-shaped bar/bulge from the thin disk.
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