  We consider a Demazure slice of type $A_{2l}^{(2)}$, that is an associated
graded piece of an infinite-dimensional version of a Demazure module. We show
that a global Weyl module of a hyperspecial current algebra of type
$A_{2l}^{(2)}$ is filtered by Demazure slices. We calculate extensions between
a Demazure slice and a usual Demazure module and prove that a graded character
of a Demazure slice is equal to a nonsymmetric Macdonald-Koornwinder polynomial
divided by its norm. In the last section, we prove that a global Weyl module of
the special current algebra of type $A_{2l}^{(2)}$ is a free module over the
polynomial ring arising as the endomorphism ring of itself.
