  Matom\"aki proved that if $\alpha\in \mathbb{R}$ is irrational, then there
are infinitely many primes $p$ such that $|\alpha-a/p|\le p^{-4/3+\varepsilon}$
for a suitable integer a. In this paper, we extend this result to all quadratic
number fields under the condition that the Grand Riemann Hypothesis holds for
their Hecke $L$-functions.
