Eccentric Jupiter

Eccentric Jupiters are gas or ice giants which have an orbital eccentricity of greater than 0.1. Roughly 7% of all stars have Eccentric Jupiters in their planetary systems.

Eccentric Jupiters with an eccentricity of greater than 0.6 would likely interfere greatly with the other bodies in the planetary system, thus making habitability of any of these bodies increasingly unlikely. Those with comparatively little eccentricity (around 0.1 to 0.2) might still allow for some planets to remain in the habitable zone of their star. These planets would be much drier than Earth, according to computer simulations.

Worldbuilding in Practice
"Jacobi is an eccentric gas giant weighing 0.64 MJ, with a radius of 1.18 RJ, orbiting the G class star Gauss. With an orbital eccentricity of 0.168, its closest approach to Gauss is at a distance of 3.03 AU, while its furthest point from the star is at a distance of 4.25 AU. Jacobi's eccentricity has cleared the Gauss system of many planets, according to computer simulations, but a few inner planets remain unharmed by Jacobi's orbit. One of these planets is the desert planet Seidel, which orbits Gauss in its habitable zone, and is home to a human colony."