His maternal grandfather was Rabbi Yiḥya Badiḥi (1803–1887), the renowned sage and author of the Questions & Responsa, Ḥen Ṭov, and a commentary on the laws of ritual slaughter of livestock, Leḥem Todah, who served as the head of Sanaa's largest seat of learning (yeshiva), held in the synagogue, Bayt Saleḥ, before he was forced to flee from Sana'a in 1846 on account of the tyrant, Abū-Zayid b. Ḥasan al-Miṣrī, who persecuted the Jews under the Imam Al-Mutawakkil Muhammad.

[4] The following year he was transferred by his father to the Beth midrash of Rabbi Avraham al-Qareh (d. 1890), where he began to learn the proper rendering for readings in the Babylonian Talmud, as this teacher is said to have been the most punctilious and astute of his generation.

In 1886, at the age of twenty, Avraham married his first wife who bore him a daughter, but they would both become ill and die during the sea-voyage from Yemen to Egypt in 1891, while en route to Palestine.

He writes of this period: “At first, we forbade [them] and made them outcasts in the community, anyone who would go again to receive any money, or any clothing, as they did before from the instigators, and even more so those who would go there to listen to their preaching on Sunday in their house of convocation.

Al-Naddaf wrote the Beit Din in Sana'a, seeking their advice, to which inquiry Mori Yihya Yitzhak Halevi replied by writing that the Yemenites are to persist in their own custom, although it differs from the other communities.

[15] In 1910, the Yemenite Jewish community in Jerusalem and in Silwan purchased on credit a parcel of ground on the Mount of Olives for burying their dead, through the good agencies of Albert Antébi and with the assistance of the philanthropist, Baron Edmond Rothschild.

Al-Naddaf made commentaries and annotations to Rabbi Yihya Saleh's Questions & Responsa Pe'ulat Sadiq, a work published by Shemuel Badiḥi in two editions.

Rabbi Avraham Al-Naddaf died on 21 February 1940 in Tel Aviv's Kerem HaTeimanim, and was buried by his three surviving sons and daughter in the Mount of Olives in Jerusalem.