  Inflows at the dusty torus and smaller scales is crucial to investigate the
process of supermassive black hole accretion. However, only few cases of
inflowing gas at small scales have been reported through redshifted broad
absorption 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 are
likely along the directions close to the axes of accretion disks. The quasars
showing inflowing Mg II NALs have on average slightly smaller Eddington ratios
when compared to the sources with outflow Mg II NALs. The upper limits of
locations of the detected NALs are at parsec scale, around the distances of
dusty tori to central SMBHs. The one possible origin of these infalling NALs is
from dusty tori. Of course, these infalling NALs can also be naturally
explained by chaotic cold accretion resulted from the nonlinear interaction of
active galactic nucleus (AGN) jets with the interstellar medium, and these cold
gaseous blobs may originally precipitate in metal-rich trailing outflows
uplifted by AGN jet ejecta. The infalling NALs may thus provide direct evidence
for cold gas precipitation and accretion in AGN feedback processes, and provide
the direct evidence of inflowing gas along the directions close to quasar jets
and at parsec scale. It does not matter whether these infalling NALs are from
the dusty tori or the interaction of AGN jets with the ISM, the infalling NALs
cannot provide sufficient fuels to power the quasars.
