Shabbat is a day of rest in Gehenna as well, but only for those who observed it.

On Shabbat the wicked in Gehenna are allowed to rest:

Every Shabbat evening, once the day has been sanctified, the criers pass through all parts of Gehenna, [proclaiming,] “Let the punishments of the wicked cease, as the holy King has come and the day is sanctified, and Shabbat provides protection to everyone.” The punishments immediately cease and the wicked ones receive a respite.

One who does not observe Shabbat will never have rest:

But the fire of Gehenna does not abate for those who never kept Shabbat. All the evil people of Gehenna ask about those [individuals], “In what way are these people, who have no rest, different from all the other wicked people who are here?” And the ones who inflict punishment answer them, “These are the wicked people who rejected the Holy One, blessed be He, and transgressed the entire Torah. Because they did not keep Shabbat there [in this world], they will never have any rest.” (Zohar 2:151a)