Muhammad (ﷺ) traveled to Yathrib (Medina) exactly one time before the Hijra.
This visit occurred when he was approximately six years old. He accompanied his mother, Aminah bint Wahb, and her servant, Umm Ayman, to visit his maternal relatives from the Banu Najjar clan. They stayed in Yathrib for one month. On the return journey to Mecca, his mother fell ill and passed away at Al-Abwa, leaving him to return to Mecca with Umm Ayman.
The Lineage of Salma bint Amr
Salma bint Amr was an Arab woman from the Banu Khazraj tribe, specifically the Banu Najjar clan.
Ethnicity: The Khazraj were Qahtani Arabs (originating from Yemen) who migrated to Yathrib (Medina). They were not ethnically Israelite.
Religion: Prior to the advent of Islam, the Banu Najjar were polytheists (pagans), worshipping idols such as Manat, though they lived in close proximity to Jewish tribes and were influenced by monotheistic ideas.
Social Status: Salma was a powerful, wealthy merchant who famously refused to marry unless she could remain in her own home in Yathrib and manage her own affairs.
She married Hashim (the Prophet’s great-grandfather) under these conditions.
The Source of Confusion (Yathrib Context)
The confusion likely stems from the demographics of Yathrib (Medina) at the time:
Jewish Dominance: Yathrib was home to three major Jewish tribes (Banu Qaynuqa, Banu Nadir, Banu Qurayza).
The Arab tribes (Aws and Khazraj) lived alongside them, formed alliances, and sometimes intermarried. "Maternal Uncles": Because Salma was from Medina, the Prophet Muhammad frequently referred to the Banu Najjar as his "maternal uncles" (akhwal). This geographic association with Medina—a city famous for its Jewish population—often leads to the mistaken assumption that his Medinan ancestors were Jewish.
Unfounded Myth (Identity) vs. Plausible Reality (Cultural/Genetic Admixture)
While Jebara’s specific claim that Salma was a "Jewish noblewoman" is historically rejected, the possibility of distant genetic admixture is not zero. However, in tribal Arabia, identity was patrilineal.
1. The "Convert" Factor (The Plausible Reality) The most likely source of "Jewish roots" in the Khazraj is not intermarriage with Israelites, but conversion.
Pre-Islamic sources confirm that some Arabs in Yathrib converted to Judaism to emulate the perceived sophistication or success of their Jewish neighbors.
It is historically possible that members of the Banu Najjar had embraced Judaism or were "Judaized Arabs." However, the sources explicitly record Salma and her immediate family as adhering to traditional Arab polytheism (or the vague monotheism of the Hanifs), not Judaism.
2. The "Alliance" Confusion (The Source of the Myth) The deep connection you mention was primarily political (Hilf), not biological.
The Banu Najjar had strong alliances with Jewish clans.
In Arabic tribal law, an ally is often treated with the same rhetoric as a kinsman. When the Prophet called the residents of Medina his "uncles," later interpreters (and modern revisionists like Jebara) may have biologically literalized a political metaphor.
3. The Salma Specifics If Salma bint Amr had been Jewish, it would have been a defining feature of her biography in the Seerah.
The early Muslim historians (Ibn Ishaq, Al-Waqidi) were meticulous about documenting who was "of the Jews" (min al-yahud) versus "of the Arabs."
They classify Salma as Khazraji (Arab).
Her refusal to leave Medina to live with Hashim in Mecca was based on her power as a clan matriarch of the Banu Najjar, a trait consistent with high-status Arab women in matriarchal-leaning clans, not specifically a Jewish trait.
You are asking about a specific biological and legal mechanism: Could a "hidden" Jewish lineage exist within an Arab tribe because of the clash between Jewish matrilineal law and Arab patrilineal law?
The short answer is: Theoretically, yes. Your logic is sound regarding how the two systems interact.
1. The "Hidden Lineage" Mechanism
You have correctly identified a historical loophole where "Jewishness" could theoretically persist in an Arab line without being socially visible.
The Conflict of Laws:
Jewish Law (Halakha): Identity is matrilineal. If the mother is Jewish, the child is Jewish, regardless of who the father is.
Arab Custom (Nasab): Identity is patrilineal. If the father is Khazraji (Arab), the child is 100% Khazraji.
The Result: If a Jewish woman from Banu Nadir married an Arab man from Banu Najjar, the child would be:
Socially/Tribally: An Arab. They would be raised with Arab customs, pagan religion, and total loyalty to the father’s tribe.
Biologically/Halakhically: Technically Jewish (by Jewish law) and carrying Jewish mitochondrial DNA.
While the mechanism is possible, the "intermarriage rate" was extremely low for three reasons:
Religious caste system: The Jewish tribes (Nadir, Qurayza) considered themselves a spiritual aristocracy. They viewed the pagan Arabs as "Gentiles" (Umiyyin) and generally refused to give their daughters to them in marriage.
The "lost" children: In the rare cases where this did happen (often through coercion or political treaties), the child was almost always raised as a pagan Arab. The Jewish identity was "erased" instantly by the father's culture.
Mitochondrial dead ends: If that child was male, the mitochondrial line stopped there. If female, it could continue, but she would be married off to another Arab, further diluting any cultural memory of Jewishness.
For Salma to be "hidden Jewish," one of these women would have to be a secret Jewess from Banu Nadir or Qaynuqa. There is no historical record of this. The early Islamic historians (like Ibn Ishaq) were obsessed with genealogy; if there was a Jewish mother in the line, they almost certainly would have recorded it, as they did with other figures (like Safiyya bint Huyayy, the Prophet's wife of Jewish descent).
Summary
Your logic: Valid. It is theoretically possible for "Halakhic Jews" to exist within Arab tribes due to the matrilineal/patrilineal mismatch.
Application to Salma: Unfounded. Her recorded maternal line is Arab (Amirah bint Sakhr).
The Reality: While there were almost certainly some Arabs in Medina who had Jewish mothers, they were assimilated into Arab paganism. They did not maintain a "crypto-Jewish" identity.