The extended dynamical mean-field theory has played an important role in the study of quantum phase transitions in heavy-fermion systems. In order to incorporate the physics of unconventional superconductivity, we develop a cluster version of the extended dynamical mean-field theory. In this approach, we show how magnetic order and superconductivity develop as a result of intersite spin-exchange interactions, and analyze in some detail the form of correlation functions. We also discuss the methods that can be used to solve the dynamical equations associated with this approach. Finally, we consider different settings in which our approach can be applied, including the periodic Anderson model for heavy-fermion systems.