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Inflows at the dusty torus and smaller scales is crucial to investigate theprocess of supermassive black hole accretion. However, only few cases ofinflowing gas at small scales have been reported through redshifted broadabsorption lines so far. Here we report 9 redshifted narrow absorption lines(NALs) of $\rm Mg^+$ ions with inflowing speeds of 1071 -- 1979 km/s, which arelikely along the directions close to the axes of accretion disks. The quasarsshowing inflowing Mg II NALs have on average slightly smaller Eddington ratioswhen compared to the sources with outflow Mg II NALs. The upper limits oflocations of the detected NALs are at parsec scale, around the distances ofdusty tori to central SMBHs. The one possible origin of these infalling NALs isfrom dusty tori. Of course, these infalling NALs can also be naturallyexplained by chaotic cold accretion resulted from the nonlinear interaction ofactive galactic nucleus (AGN) jets with the interstellar medium, and these coldgaseous blobs may originally precipitate in metal-rich trailing outflowsuplifted by AGN jet ejecta. The infalling NALs may thus provide direct evidencefor cold gas precipitation and accretion in AGN feedback processes, and providethe direct evidence of inflowing gas along the directions close to quasar jetsand at parsec scale. It does not matter whether these infalling NALs are fromthe dusty tori or the interaction of AGN jets with the ISM, the infalling NALscannot provide sufficient fuels to power the quasars.

The detections of inflowing gas from narrow absorption lines at the parsec scale