  We characterize braided commutative Yetter-Drinfeld $C^*$-algebras over weak
Hopf $C^*$-algebras in categorical terms. Using this, we then study quotient
type coideal subalgebras of a given weak Hopf $C^*$-algebra $\mathcal G$ and
coideal subalgebras invariant with respect to the adjoint action of $\mathcal
G$. Finally, as an example, we explicitly describe quotient type coideal
subalgebras of the weak Hopf $C^*$-algebras associated with Tambara-Yamagami
categories.
