We introduce a generalized atomic system of N-level \((N-2)\) V-configuration atom, with integer \(N>2\) , interacting with a single mode field in the presence of multi-photon transitions and Kerr medium. We solve this system by virtue of supersymmetric (SUSY) unitary transformation and show that it possesses SUSY structure and define its SUSY generators and perform the diagonalization of the corresponding Hamiltonian. We construct the eigenstates and eigenvalues of this system when the atom and the field mode are initially prepared in two different cases. We investigate some quantum aspects of the considered system, namely, the time evolution of the atomic population inversion of the system, the evolution of the Mandel M-parameter and the distribution Husimi Q-function of the field. We show the influence of the detuning and Kerr medium parameters on their behavior for some different N, where e.g., for \(N=5\) we obtain the results of the five-level triple V-type system. We end with some discussions and conclusion.
