We consider the trigonometric Felderhof model of free fermions in an external field, on afinite lattice with domain wall boundary conditions. The vertex weights are functions ofrapidities and external fields.We obtain a determinant expression for the partition function in the special case where thedependence on the rapidities is eliminated, but for general external field variables. This determinantcan be evaluated in product form. In the homogeneous limit, it is proportional to a 2-Todaτ function.Next, we use the algebraic Bethe ansatz factorized basis to obtain a productexpression for the partition function in the general case with dependence on allvariables.