Diophantine approximation with prime denominator in quadratic number fields under GRH

Matomäki proved that if $\alpha \in \mathbb{R}$ is irrational, then there are infinitely many primes $p$ such that $\mathrm{\mid }\alpha -a\mathrm{/}p\mathrm{\mid }\le p^{-4\mathrm{/}3+\epsilon }$ 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.