  In this paper, we give a combinatorial realization of the crystal basis of a
quantum Weyl module over a quantum affine algebra of type $A_{2n}^{(2)}$, and a
representation-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 dominant
weight and $P_{\lambda}^{A_{2n}^{(2)}}(q,t)$ denotes the specific
specialization of the symmetric Macdonald-Koornwinder polynomial
$P_{\lambda}(q,t_1, t_2, t_3, t_4, t_5)$. More precisely, as some results for
untwisted affine types, the set of all ($A_{2n}^{(2)}$-type) quantum
Lakshmibai-Seshadri paths of shape $\lambda$, which is described in terms of
the finite Weyl group $W$, realizes the crystal basis of a quantum Weyl module
over a quantum affine algebra of type ${A_{2n}^{(2)}}$ and its graded character
is equal to the specialization $P_{\lambda}^{A_{2n}^{(2)}} (q,0)$ of the
symmetric Macdonald-Koornwinder polynomial.
