  In this paper, we study the interaction between a three-level atom and a
quantized single-mode field with $` `$intensity-dependent coupling$"$ in a $`
`$Kerr medium$"$.
  The three-level atom is considered to be in a $\Lambda$-type configuration.
  Under particular initial conditions, which may be prepared for the atom and
the field, the dynamical state vector of the entire system will be explicitly
obtained, for arbitrary nonlinearity function $f(n)$ associated to any physical
system.
  Then, after evaluating the variation of the field entropy against time, we
will investigate the quantum statistics as well as some of the nonclassical
properties of the introduced state. During our calculations we investigate the
effects of intensity-dependent coupling, Kerr medium and detuning parameters on
the depth and domain of the nonclassicality features of the atom-field state
vector. Finally, we compare our obtained results with those of $V$-type
three-level atoms.
