Are overlapping generation models (OLG) extensions of a dynamic stochastic general equilibrium (DSGE) model? Or aren't these DSGE per se?
You can find OLG models that do not classify as DSGE (in particular, the model might not be stochastic) as well as DSGE with overlapping generations (contrary to those with infinitely lived agents).
You can find more detail on this on this working paper by Assous and Duarte (2017), as they note
In the early 1980s, when the real business cycle macroeconomists brought one single model (a perfectly competitive growth model with infinite-lived agents, flexible prices, and perfect information) to bear on any macroeconomic issue, several macroeconomists were working with OLG models and addressing business fluctuations matters. Besides the efficiency issue, the model seemed to have much more to offer. New classical economists such as Wallace and Lucas saw in the OLG model the possibility to develop new microfounded models of fiat money without postulating that money balances enter the utility function of agents. At about the same time, other macroeconomists discovered that OLG models give room for either deterministic or stochastic oscillatory trajectories. Endogenous cycles and chaos as well as sunspot equilibria were then shown to occur in the presence of perfectly competitive product market devoid of any nominal price rigidities. Gradually over time, important contributors to that literature — most notably, for our interests here, is Woodford — strove to transfer OLG conclusions to infinite-lived agents models. In this context, new dynamic models with market imperfections were developed, initially with flexible prices, that eventually became the hallmark of the sticky price, DSGE macroeconomics (earlier referred to as the new neoclassical synthesis).