Entropy increase of both system and surroundings
We don't need to go to nuclear fusion to find an example. Lots of chemical reactions meet your criteria of being both exothermic (releasing heat to the surroundings) and increasing the entropy of the system.
A reaction is spontaneous if the free energy change of the reaction is negative ($\Delta_rG &lt;0)$.The free energy change of a reaction at constant temperature is equal to the sum of the enthalpy change ($\Delta_rH$) and the temperature multiplied by the negative entropy change ($-T\Delta_rS$):
$$\Delta_rG = \Delta_rH - T\Delta_rS$$
One way for $\Delta_rG$ to be negative is for $\Delta_rH$ to be negative and $\Delta_rS$ to be positive. In a reaction conducted at constant pressure, the enthalpy change $\Delta_rH$ is equal to the heat exchanged between the system (reactants) and the surroundings. When $\Delta_rH &lt;0$, the reaction is exothermic.
To find examples that meen your criteria, you only need a source of standard entropy and ethalpy data so that you can calculate $\Delta_rH$ and $\Delta_rS$ for a reaction. There are many such examples of reactions that are exothermic and have a positive entropy change of the system. Below is a simple example:
$$\ce{C(s) + O2(g) -&gt; CO2(g)}$$
Use the NIST Chemistry Webbook, here are the standard enthalpies of formation and standard entropies of formation for carbon, oxygen, and carbon dioxide:
$$\begin{array}{|l|c|c|} \hline
 &amp; \Delta_fH^\circ\ \mathrm{(kJ/mol)} &amp; \Delta S^\circ\ \mathrm{J\cdot K/mol} \\ \hline
\ce{C(g)} &amp; 0 &amp; 5.8 \\ 
\ce{O2(g)} &amp; 0 &amp; 205.15 \\ 
\ce{CO2(g)} &amp; -383.52 &amp; 213.79 \\ \hline
\Delta_r &amp; -383.52 &amp; 2.84 \\ \hline
\end{array}$$
At all temperatures, this reaction is exothermic and has a positive entropy change for the  system.