  The scalar products, form factors and correlation functions of the XXZ spin
chain with twisted (or antiperiodic) boundary condition are obtained based on
the inhomogeneous $T-Q$ relation and the Bethe states constructed via the
off-diagonal Bethe Ansatz. It is shown that the scalar product of two off-shell
Bethe states, the form factors and the two-point correlation functions can be
expressed as the summation of certain determinants. The corresponding
homogeneous limits are studied. The results are also checked by the numerical
calculations.
