  A first search for the $\it{\Xi}_{bc}^{+}\to J/\it{\psi}\it{\Xi}_{c}^{+}$
decay is performed by the LHCb experiment with a data sample of proton-proton
collisions, corresponding to an integrated luminosity of $9\,\mathrm{fb}^{-1}$
recorded at centre-of-mass energies of 7, 8, and $13\mathrm{\,Te\kern -0.1em
V}$. Two peaking structures are seen with a local (global) significance of
$4.3\,(2.8)$ and $4.1\,(2.4)$ standard deviations at masses of
$6571\,\mathrm{Me\kern -0.1em V\!/}c^2$ and $6694\,\mathrm{Me\kern -0.1em
V\!/}c^2$, respectively. Upper limits are set on the $\it{\Xi}_{bc}^{+}$ baryon
production cross-section times the branching fraction relative to that of the
$B_{c}^{+}\to J/\it{\psi} D_{s}^{+}$ decay at centre-of-mass energies of 8 and
$13\mathrm{\,Te\kern -0.1em V}$, in the $\it{\Xi}_{bc}^{+}$ and in the
$B_{c}^{+}$ rapidity and transverse-momentum ranges from 2.0 to 4.5 and 0 to
$20\,\mathrm{Ge\kern -0.1em V\!/}c$, respectively. Upper limits are presented
as a function of the $\it{\Xi}_{bc}^{+}$ mass and lifetime.
