In this article, we consider the problem of finding upper bounds on the minimum norm of representatives in residue classes in quotient $O/I$ , where $I$ is an integral ideal in the maximal order $O$ of a number field $K$ . In particular, we answer affirmatively a question of Konyagin and Shparlinski [KS], stating that an upper bound $o(N(I))$ holds for most ideals $I$ , denoting $N(I)$ the norm of $I$ . More precise statements are obtained, especially when $I$ is prime. We use the method of exponential sums over multiplicative groups, essentially exploiting some new bounds obtained by the authors