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In this paper, we give a combinatorial realization of the crystal basis of aquantum Weyl module over a quantum affine algebra of type $A_{2n}^{(2)}$, and arepresentation-theoretic interpretation of the specialization$P_{\lambda}^{A_{2n}^{(2)}} (q,0)$ of the symmetric Macdonald polynomial$P_{\lambda}^{A_{2n}^{(2)}} (q,t)$ at $t=0$, where $\lambda$ is a dominantweight and $P_{\lambda}^{A_{2n}^{(2)}}(q,t)$ denotes the specificspecialization of the symmetric Macdonald-Koornwinder polynomial$P_{\lambda}(q,t_1, t_2, t_3, t_4, t_5)$. More precisely, as some results foruntwisted affine types, the set of all ($A_{2n}^{(2)}$-type) quantumLakshmibai-Seshadri paths of shape $\lambda$, which is described in terms ofthe finite Weyl group $W$, realizes the crystal basis of a quantum Weyl moduleover a quantum affine algebra of type ${A_{2n}^{(2)}}$ and its graded characteris equal to the specialization $P_{\lambda}^{A_{2n}^{(2)}} (q,0)$ of thesymmetric Macdonald-Koornwinder polynomial.

Quantum Lakshmibai-Seshadri paths and the specialization of Macdonald polynomials at $t=0$ in type $A_{2n}^{(2)}$