The criteria of the ground-state stability and correlations in finite size two-component (two orbital) fermions in Hubbard-like model are obtained for an attractive potential in a strong magnetic field at half-filling and for two holes near full band filling, where it is possible to get an exact result for any dimension. The ground-state properties and density correlation functions of two holes with different masses in 1d, 2d and 3d lattices are found.
