Which moon has a magnetic field of its own?

Ganymede, the largest moon in the Solar System and the only one known to generate its own magnetic field - which means a molten, convecting iron core, like a planet. Nothing else that orbits a planet does this.

The result is a magnetosphere sitting inside another magnetosphere. Jupiter's field is by far the largest structure in the Solar System after the Sun's, and Ganymede carves a bubble within it - a nested arrangement that exists nowhere else anyone has looked, and which produces auroras at the moon's poles. Watching those auroras rock back and forth is how Hubble inferred a subsurface ocean: a conducting salty layer under the ice damps the swing, and the amount of damping gives you the ocean.

That ocean may hold more water than all of Earth's, under perhaps 150 kilometres of ice, possibly layered between different phases of ice at different pressures. The European JUICE mission, launched in 2023, will eventually enter orbit around it in the mid-2030s - the first spacecraft ever to orbit a moon other than our own.