  We study the quantization for a class of in-homogeneous self-similar measures
$\mu$ supported on self-similar sets. Assuming the open set condition for the
corresponding iterated function system, we prove the existence of the
quantization dimension for $\mu$ of order $r\in(0,\infty)$ and determine its
exact value $\xi_r$. Furthermore, we show that, the $\xi_r$-dimensional lower
quantization coefficient for $\mu$ is always positive and the upper one can be
infinite. We also give a sufficient condition to ensure the finiteness of the
upper quantization coefficient.
