Matomäki 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.
