Let \(\mathfrak g\) be a finite dimensional simple Lie algebra over \(\mathbb C\) , and let \(\ell \) be a positive integer. In this paper, we construct the quantization \(K_{\hat{\mathfrak {g}},\hbar }^\ell \) of the parafermion vertex algebra \(K_{\hat{\mathfrak {g}}}^\ell \) as an \(\hbar \) -adic quantum vertex subalgebra inside the simple quantum affine vertex algebra \(L_{\hat{\mathfrak {g}},\hbar }^\ell \) . We show that \(L_{\hat{\mathfrak {g}},\hbar }^\ell \) contains an \(\hbar \) -adic quantum vertex subalgebra isomorphic to the quantum lattice vertex algebra \(V_{\sqrt{\ell }Q_L}^{\eta _\ell }\) , where \(Q_L\) is the lattice generated by the long roots of \(\mathfrak g\) . Moreover, we prove the double commutant property of \(K_{\hat{\mathfrak {g}},\hbar }^\ell \) and \(V_{\sqrt{\ell }Q_L}^{\eta _\ell }\) in \(L_{\hat{\mathfrak {g}},\hbar }^\ell \)
