  The main purpose of this paper is to give a combinatorial realization of
Kirillov-Reshetikhin (KR simply) crystals $B^{r, s}$ for type
$\text{E}_n^{(1)}$ with a minuscule node $r$ and $s \ge 1$. To do this, we
describe explicitly the crystal of the quantum nilpotent subalgebra associated
with the translation by the negative of the $r$-th fundamental weight. Then the
crystal can be extended as an affine crystal, in which a certain subcrystal
characterized by the $\varepsilon_r^*$-statistic is isomorphic to $B^{r,s}$ as
an affine crystal, where $\varepsilon_r^*$ is also realized precisely in terms
of triple and quadruple paths.
