  $q$-Yangians can be viewed as quantum deformations of the upper triangular
loop Lie algebras, and also be viewed as deformation of the Yangian algebra. In
this paper, we study the twisted $q$-Yangians as coideal subalgebras of the
quantum affine algebra introduced by Molev, Ragoucy and Sorba. We investigate
the invariant theory of the quantum symmetric spaces in affine types $AI, AII$
and use the Sklyanin determinants to study the invariant theory and show that
they also obey classical type identities similar to the quantum coordinate
algebras of finite types.
