  Given a domain $\Omega$ in $\mathbb{C}^n$ and a collection of test functions
$\Psi$ on $\Omega$, we consider the complex-valued $\Psi$-Schur-Agler class
associated to the pair $(\Omega,\,\Psi)$. In this article, we characterize
interpolating sequences for the associated Banach algebra of which the
$\Psi$-Schur-Agler class is the closed unit ball. When $\Omega$ is the unit
disc $\mathbb{D}$ in the complex plane $\mathbb{C}$ and the class of test
function includes only the identity function on $\mathbb{D}$, the
aforementioned algebra is the algebra of bounded holomorphic functions on
$\mathbb{D}$ and in this case, our characterization reduces to the well known
result by Carleson. Furthermore, we present several other cases of the pair
$(\Omega,\,\Psi)$, where our main result could be applied to characterize
interpolating sequences which also show the efficacy of our main result.
