Which type of fusion occurs in the red giant phase?
A red giant star is fusing Hydrogen into Helium.
Main sequence stars are fusing Hydrogen into Helium in their cores. If the star is less than eight solar masses, the supply of Hydrogen in the core gets to a level where the core is mainly Helium and Hydrogen fusion can no longer occur.
When Hydrogen fusion stops, the Helium core collapses under gravity. The layers of Hydrogen in the shell around the core get hot enough to restart Hydrogen fusion. This causes the outer layer of the star to expand into a red giant.
So, a red giant is fusing Hydrogen into Helium in a shell around the Helium core.