Is expiation (kaffarah) obligatory for one who swore an oath concerning something they did not do, having forgotten it, and should they correct their statements after realizing the mistake, or remain silent?

If you swore forgetfully that you had done something, this falls under "Laghw al-Yamin" (unintentional or vain oaths) according to most scholars, and no expiation is due from you for it. This has been narrated from Ibn Abbas, Abu Hurairah, Malik, Abu Hanifa, and Al-Thawri, and Muslims have unanimously agreed that no expiation is required for Laghw al-Yamin.