  We give a systematical study on the recently reported excited charm and
charm-strange mesons with potential $1^-$ spin-parity, including the
$D^*_{s1}(2700)^+$, $D^*_{s1}(2860)^+$, $D^*(2600)^0$, $D^*(2650)^0$,
$D^*_1(2680)^0$ and $D^*_1(2760)^0$. The main strong decay properties are
obtained by the framework of Bethe-Salpeter (BS) methods. Our results reveal
that the two $1^-$ charm-strange mesons can be well described by the further
$2^3\!S_1$-$1^3\!D_1$ mixing scheme with a mixing angle of $8.7^{+3.9}_{-3.2}$
degrees. The predicted decay ratio $\frac{\mathcal{B}(D^*K)}{\mathcal{B}(D~K)}$
for $D^*_{s1}(2860)$ is $0.62^{+0.22}_{-0.12}$.~$D^*(2600)^0$ can also be
explained as the $2^3\!S_1$ predominant state with a mixing angle of
$-(7.5^{+4.0}_{-3.3})$ degrees. Considering the mass range, $D^*(2650)^0$ and
$D^*_1(2680)^0$ are more likely to be the $2^3\!S_1$ predominant states,
although the total widths under both the $2^3\!S_1$ and $1^3\!D_1$ assignments
have no great conflict with the current experimental data. The calculated width
for LHCb $D^*_1(2760)^0$ seems about 100 \si{MeV} larger than experimental
measurement if taking it as $1^3\!D_1$ or $1^3\!D_1$ dominant state $c\bar u$.
The comparisons with other calculations and several important decay ratios are
also present. For the identification of these $1^-$ charm mesons, further
experimental information, such as
$\frac{\mathcal{B}(D\pi)}{\mathcal{B}(D^*\pi)}$ are necessary.
