  The generalization of the Yang-Baxter equations (YBE) in the presence of Z_2
grading along both chain and time directions is presented and an integrable
model of t-J type with staggered disposition along a chain of shifts of the
spectral parameter is constructed. The Hamiltonian of the model is computed in
fermionic formulation. It involves three neighbour site interactions and
therefore can be considered as a zig-zag ladder model. The Algebraic Bethe
Ansatz technique is applied and the eigenstates, along with eigenvalues of the
transfer matrix of the model are found. In the thermodynamic limit, the lowest
energy of the model is formed by the quarter filling of the states by fermions
instead of usual half filling.
