Final answer:
Hermes, known as Mercury in Roman mythology, is the god with a winged cap and winged sandals, symbolizing his role as the swift messenger of the gods and guiders of souls to the underworld.
Step-by-step explanation:
The god with a winged cap and winged sandals is known as Hermes in Greek mythology, and as Mercury in Roman mythology. Hermes was known as the messenger of the gods due to his speedy travel capabilities, which were aided by his winged accessories. These allowed him to fly swiftly as a bringer of messages and a guide for souls to the underworld. The winged sandals also played a role in the stories of other characters, such as Perseus, who received them as a tool to help him in his quest to defeat Medusa.