  We examine conditions under which there exists a non-constant family of
Galois branched covers of curves over an algebraically closed field $k$ of
fixed degree and fixed ramification locus, under a notion of equivalence
derived from considering linear series on a fixed smooth proper source curve
$X$. We show such a family exists precisely when the following conditions are
satisfied: $\operatorname{char}(k)=p>0$, $X$ is isomorphic to $\mathbb{P}^1_k$,
there is a unique ramification point, and the Galois group is
$(\mathbb{Z}/p\mathbb{Z})^m$ for some integer $m>0$.
