By definition the Galapagos Islands are not on a continent.

The two main types of islands are continental islands, which are formed from the same landmass as a nearby continent, and oceanic islands, which are formed from underwater volcanic activity or coral reefs. Continental islands tend to be larger and closer to continents, while oceanic islands are typically smaller and more isolated.

The main types of islands are continental islands, which are part of a continental shelf; oceanic islands, which are formed by volcanic activity; and coral islands, which are formed from coral reefs. There are also artificial islands, which are man-made structures typically created for expansion or development purposes.

Rocks and snow

I think you mean what Indian Ocean country of islands has its own continental shelf - It it Seychelles