  In this paper the interaction Lagrangian of a superparticle with an external
chiral superfield $\Phi(x,\theta,\bar{\theta})$,invariant with respect to the
global supersymmetry, is proposed. The kinematics of the superparticle is
defined in an extended superspace described by superspace coordinates
$(x_{\mu},\theta_{\alpha},\bar{\theta}_{\alpha})$, where $x_{\mu}$ are pure
bosonic coordinates, $\mu=0,\ldots,3$; $\theta_{\alpha}$ and
$\bar{\theta}_{\alpha}$ are additional fermionic Grassmann-valued spinors. With
the purpose of the construction of the required Lagrangian, chiral analogues of
the supervector $A_{\mu}(x,\theta,\bar{\theta})$ and superspinor
$A_{\alpha}(x,\theta,\bar{\theta})$,
$\bar{A}_{\dot{\alpha}}(x,\theta,\bar{\theta})$ gauge fields are introduced,
which are also matrices in color space. The problem considered in this paper is
the further step in deriving the dynamical equations of motion for a spin
color-charged particle moving in an external fermionic matter field. These
equations of motion are of fundamental importance, for example, when taking
into account the influence of fermionic background fields induced in a hot
quark-gluon plasma (QGP) by thermal fluctuations on the dynamics of hard
color-charged partons crossing the QGP. In turn, the solution of this problem
will make it possible, at least at the qualitative level, to advance in the
study of the motion in the external fermion matter field of such a complex
physical object as a string.
