  We give conditions for minimality of $\mathbb Z/N\mathbb Z$ extensions of a
rotation of angle $\alpha$ with one marked point, solving the problem for any
prime $N$: for $N=2$, these correspond to the Veech 1969 examples, for which a
necessary and sufficient condition was not known yet. We provide also a word
combinatorial criterion of minimality valid for general interval exchange
transformations, which applies to $\mathbb Z/N\mathbb Z$ extensions of any
interval exchange transformation with any number of marked points. Then we give
a condition for unique ergodicity of these extensions when the initial interval
exchange transformation is linearly recurrent and there are one or two marked
points.
