What type of oath did the questioner swear that he did not say a specific thing, knowing that he did say it but forgot, and what is its expiation?

This oath pertains to a past event and is not binding; therefore, according to the preponderant opinion, no expiation (kaffara) is required for it. If you swore believing yourself to be truthful, then there is no sin upon you. However, if you swore falsely and intentionally, then you must repent to Allah.

Ibn Qudamah mentioned that oaths are of four types: 1. The Binding Oath (al-Yamin al-Mun'aqidah): This is an oath concerning a future, conceivable event, and it necessitates expiation if broken. 2. Vain Oath (Lagw al-Yamin): There is no expiation for it, and it has two types: That which slips from the tongue unintentionally. Swearing about something believing it to be true, only for it to turn out otherwise. 3. The Immersive/Perjurious Oath (Yamin al-Ghamus): This is a false oath sworn by someone who knows it to be false. There is no expiation for it, according to the apparent view of the madhhab, because it is not binding. However, it is one of the major sins and requires repentance. 4. The Expiable Oath (al-Yamin al-Mukaffarah): Ibn Qudamah mentioned this within the category of the binding oath, and it is the one for which expiation is required upon breaking it.