  The microcanonical transfer matrix is used to study the distribution of the
Fisher zeros of the $Q>2$ Potts models in the complex temperature plane with
nonzero external magnetic field $H_q$. Unlike the Ising model for $H_q\ne0$
which has only a non-physical critical point (the Fisher edge singularity), the
$Q>2$ Potts models have physical critical points for $H_q<0$ as well as the
Fisher edge singularities for $H_q>0$. For $H_q<0$ the cross-over of the Fisher
zeros of the $Q$-state Potts model into those of the ($Q-1$)-state Potts model
is discussed, and the critical line of the three-state Potts ferromagnet is
determined. For $H_q>0$ we investigate the edge singularity for finite lattices
and compare our results with high-field, low-temperature series expansion of
Enting. For $3\le Q\le6$ we find that the specific heat, magnetization,
susceptibility, and the density of zeros diverge at the Fisher edge singularity
with exponents $\alpha_e$, $\beta_e$, and $\gamma_e$ which satisfy the scaling
law $\alpha_e+2\beta_e+\gamma_e=2$.
