While not exactly the sub-moon you're looking for there are some interesting objects that come close. Co-orbital moons, like Saturn's Janus and Epimetheus, are

While not exactly the sub-moon you're looking for there are some interesting objects that come close. Co-orbital moons, like Saturn's Janus and Epimetheus, are moons that are in stable orbit-swapping configurations. https://en.wikipedia.org/wiki/Co-orbital_configuration#Co-orbital_moons https://en.wikipedia.org/wiki/Co-orbital_configuration#Co-or... Then you've got asteroids that are contact binaries that also have moons, like 216 Kleopatra. https://en.wikipedia.org/wiki/216_Kleopatra https://en.wikipedia.org/wiki/216_Kleopatra And finally, you have 624 Hektor, which is a Trojan of Jupiter (stable solar orbit near Jupiter's L4 Lagrange point), that is a a likely contact binary that has a moon. So it's orbiting the Sun, while "orbiting" Jupiter's L4 point, while all 3 components (the two halves of the contact binary, and their moon) orbit the center of mass of their own little 'Hector system'. https://en.wikipedia.org/wiki/624_Hektor https://en.wikipedia.org/wiki/624_Hektor