  We conduct an investigation on the $1P$- and $2P$-wave charmed baryons using
the methods of QCD sum rules and light-cone sum rules within the framework of
heavy quark effective theory. Our results suggest that the $\Lambda_c(2910)^+$,
$\Lambda_c(2940)^+$, and $\Xi_c(3123)^+$ can be well interpreted as the
$2P$-wave charmed baryons of $J^P=1/2^-$ and $3/2^-$, belonging to the $SU(3)$
flavor $\mathbf{\bar 3}_F$ representation. Moreover, the $\Xi_c(3123)^+$
possesses a partner state characterized by $J^P=1/2^-$, denoted as
$\Xi_c(1/2^-,2P)$. Our analysis predicts its mass and width to be
$m_{\Xi_c(1/2^-,2P)} - m_{\Xi_c(3123)^+} = -18\pm{7}$MeV and
$\Gamma_{\Xi_c(2P,1/2^-)}=31^{+170}_{-27}$MeV, with $m_{\Xi_c(3123)^+} =
3122.9\pm{1.3}$MeV. We propose to search for it in the $\Xi_c(1/2^-,2P)\to
\Sigma_c K$ decay channel.
