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Matom\"aki proved that if $\alpha\in \mathbb{R}$ is irrational, then thereare 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 quadraticnumber fields under the condition that the Grand Riemann Hypothesis holds fortheir Hecke $L$-functions.

Diophantine approximation with prime denominator in quadratic number fields under GRH