  A search for the exotic meson $X(5568)$ decaying into the $B^0_s \pi^{\pm}$
final state is performed using data corresponding to $9.6 \textrm{fb}^{-1}$
from $p{\bar p}$ collisions at $\sqrt{s} = 1960$ GeV recorded by the Collider
Detector at Fermilab. No evidence for this state is found and an upper limit of
6.7\% at the 95\% confidence level is set on the fraction of $B^0_s$ produced
through the $X(5568) \rightarrow B^0_s \, \pi^{\pm}$ process.
