  We study the semi-exclusive production of $\pi^\pm B_s^0$ pairs in hadron
colliders which is associated with the $X(5568)$ structure observed by the D0
Collaboration in 2016, but that was not confirmed by LHCb and CMS later. The
reason of its appearance in the D0 and absence in LHCb and CMS is discussed in
this letter. In a semi-exclusive process, one might miss the third particle
which is produced together with the $\pi^\pm B_s^0$ simultaneously. In the
three-body Dalitz plot, once the remaining region is narrow enough after the
kinematic cuts, its reflection to another invariant mass distribution will
accumulate a large number of events within a specific energy region. If there
is an enhancement in the remaining region, it will make the reflection
structure more pronounced. The precise line shape of the reflection will depend
on the specific interaction form. A combined study of different cone cuts and
the low-energy dynamics, e.g. the Landau singularity, demonstrates that the
$X(5568)$ structure could come from this kinematic reflection. This conclusion
can be checked by both searching for the enhancement in another invariant mass
distribution, such as $B_s^0\bar{B}^0$, and the cone cut dependence of the
$X(5568)$ mass. Such a combined study can be used to distinguish the effects of
the triangle singularity from a genuine state. We also propose how to avoid
this kinematic reflection in future experimental analysis.
