  We continue the investigation of the anomalous dimension of subleading-power
$N$-jet operators. In this paper, we focus on the operators with fermion number
one in each collinear direction, corresponding to quark (antiquark) initiated
jets in QCD. We investigate the renormalization effects induced by the soft
loop and compute the one-loop mixing of time-ordered products involving
power-suppressed SCET Lagrangian insertions into $N$-jet currents through soft
loops. We discuss fermion number conservation in collinear directions and
provide explicit results for the collinear anomalous dimension matrix of the
currents. The Feynman rules for the power-suppressed SCET interactions in the
position-space formalism are collected in an appendix.
