  This article investigates congruences of $\mathfrak{p}$-adic representations
arising from effective $A$-motives defined over a global function field $K$. We
give a criterion for two congruent $\mathfrak{p}$-adic representations coming
from strongly semi-stable effective $A$-motives to be isomorphic up to
semi-simplification when restricted to decomposition groups of suitable places
of $K$. This is a function field analog of Ozeki-Taguchi's criterion for
$\ell$-adic representations of number fields. Motivated by a non-existence
conjecture on abelian varieties over number fields stated by Rasmussen and
Tamagawa, we also show that there exist no strongly semi-stable effective
$A$-motives with some constrained.
