"On the day of the Conquest, the Prophet (ﷺ) entered Makkah, and he was wearing a black 'Imamah."

THere are narrations on this topic from 'Ali, 'Amr bin Huraith, Ibn 'Abbas, Rukanah.

The Hadith is Jabir is Hasan Sahih Hadith.
Jami` at-Tirmidhi Book 24, Hadith 16
← Previous Hadith That the Prophet (ﷺ) said: "On the day of His Lord spoke to him, Musa was wearing a wool Kisa', a wool Jubbah, a wool Kummah, wool pants, and his sandals were made of the skin of a dead donkey."

This Hadith is Gharib, we do not know of it except from the the narration of Humaid Al-A'raj. And Humaid - Ibn 'Ali Al-A'raj - I Heard Muhammad saying: "Humaid bin 'Ali Al-A'raj is Munkar in Hadith." While Humaid ibn Qais Al-A'raj Al-Makki, the companion of Mujahid is trustworthy. The Kummah is a small cap.

Jami` at-Tirmidhi Book 24, Hadith 15 Next Hadith → That Ibn 'Umar said: "When the Messenger of Allah (ﷺ) would wear an 'Imamah would hang between his shoulders."

Nafi' said: "Ibn 'Umar would hang his 'Imamah between his shoulders." 'Ubaidullah said: "And I saw Al-Qasim and Salim doing that."

This Hadith is Hasan Gharib. And there is something on this topic from 'Ali. And this Hadith of 'Ali about this is not correct due to its chain.

Jami` at-Tirmidhi Book 24, Hadith 17