Mushaf-e-Ali refers to the compiled version of the Qur'an as collected by Imam Ali (عليه السلام) after the passing of the Prophet Muhammad (صلى الله عليه وآله). This version is believed to have been a collection of the Qur'an in its entirety, which Imam Ali wrote down personally, following the guidance of Allah's revelations as they were revealed to the Prophet Muhammad. The codex was written by Imam Ali in a manner that adhered strictly to the original revelation, and it was said to have been compiled between two boards, which is an indication of the method of its preservation and collection.

According to a narration in al-Kafi, a man recited the Qur'an to Imam Abu Abdillah (عليه السلام), but it was not in the manner that the people commonly recite it. Imam Abu Abdillah instructed him to desist and to recite the Qur'an the way the masses do until the Qaim (عليه السلام) rises. At that time, the true recitation of the Qur'an, as it was originally revealed, would be made known, and the Mushaf that Imam Ali had compiled would be revealed once again.

Additionally, it is mentioned that when Imam Ali completed the compilation of the Qur'an, he presented it to the people, saying that this was the Qur'an as it was revealed to Prophet Muhammad, and he had gathered it between two boards. The people, however, rejected it, stating that they already had a codex in which the Qur'an was gathered. Imam Ali responded, saying that they would never see this Mushaf again, and that his duty was simply to inform them about it. 

Furthermore, it is narrated that during the time when the Prophet passed away and the issue of succession arose, Imam Ali began compiling the Qur'an in order to preserve it from distortion. However, when Imam Ali saw that the people had pledged allegiance to Abu Bakr, he decided to complete the compilation of the Qur'an before responding to the summons for allegiance. He declared that he would not come out until he had finished compiling the Qur'an, underlining the importance of preserving the true text of the Qur'an.

In summary, the Mushaf-e-Ali represents the original compilation of the Qur'an as gathered and written down by Imam Ali (عليه السلام) during a period of political upheaval, ensuring that the Qur'an remained in its authentic form. The narration emphasizes that this compilation was distinct from the versions accepted by the majority, and that it would be revealed only with the coming of Imam Mahdi (عليه السلام).

References:
1. Muʿjam al-Aḥādīth al-Muʿtabara, H541
2. Muʿjam al-Aḥādīth al-Muʿtabara, H542