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.
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