Let \(\pi\) be a non-Desarguesian semifield plane of order \(p^ n\), where \(p\) is an odd prime number and \(n \geq 3\). Let \(G\) be the autotopism group of \(\pi\) relative to an autotopism triangle \(\Delta\). We prove that if the group \(\overline G\) induced by \(G\) on a side of \(\Delta\) is transitive on the non-vertex points of that side, then \(\pi\) is a generalized twisted field plane, except possibly when \(p^ n=3^ 6\) and \(\overline G \cong SL(2,13)\). From this result it follows that the non- Desarguesian semifield planes of rank 3 are, in general, generalized twisted field planes. Another consequence is that it strengthens Theorem A in the paper by \textit{M. J. Ganley} and \textit{V. Jha} [Arch. Math. 47, 379-384 (1986; Zbl 0596.51002)], and so we have that if a finite translation plane of odd characteristic admits a collineation group that fixes a point \(L\) on the line at infinity \(\ell_ \infty\) and acts 2- transitively on \(\ell_ \infty - \{L\}\), then the plane is Desarguesian or a generalized twisted field plane.