  We provide comprehensive investigations for the mass spectrum of exotic
open-flavor charmed/bottom $sq\bar q\bar c$, $qq\bar q\bar c$, $sq\bar q\bar
b$, $qq\bar q\bar b$ tetraquark states with various spin-parity assignments
$J^P=0^+, 1^+, 2^+$ and $0^-, 1^-$ in the framework of QCD sum rules. In the
diquark configuration, we construct the diquark-antidiquark interpolating
tetraquark currents using the color-antisymmetric scalar and axial-vector
diquark fields. The stable mass sum rules are established in reasonable
parameter working ranges, which are used to give reliable mass predictions for
these tetraquark states. We obtain the mass spectra for the open-flavor
charmed/bottom $sq\bar q\bar c$, $qq\bar q\bar c$, $sq\bar q\bar b$, $qq\bar
q\bar b$ tetraquark states with various spin-parity quantum numbers. In
addition, we suggest searching for exotic doubly-charged tetraquarks, such as
$[sd][\bar u\bar c]\to D_s^{(\ast)-}\pi^-$ in future experiments at facilities
such as BESIII, BelleII, PANDA, LHCb and CMS, etc.
