The definition of who is a Jew varies according to whether it is being considered by Jews based on normative religious statutes, self-identification, or by non-Jews for other reasons. Because Jewish identity can include characteristics of an ethnicity, a religion, and citizenship, the definition of who is a Jew has varied, depending on whether a religious, sociological, or ethnic aspect was being considered. The issue has given rise to legal controversy, especially in Israel, but also outside of Israel. There have been court cases in Israel since 1962 which have had to address the question. Also, in 2009 a United Kingdom court had to consider whether the question was a racial issue for the purpose of Race Relations Act 1976, in the case R(E) v Governing Body of JFS.
According to the Mishnah, the oldest codified normative definition used by Jews for self-identification, a person is matrilineally a Jew by birth, or becomes one through conversion to Judaism. Adherence to this definition has been challenged since the emergence of the Karaite sect, emergence of modern groups in Judaism since the 19th century, and the creation of Israel in 1948. Issues that have been raised reflect:
The Jewish ethnonym in Hebrew is יהודים Yehudim (plural of יהודי Yehudi) which is the origin of the English word Jew. The Hebrew name is derived from the region name Judah (Yehudah יהודה). Originally the name referred to the territory allotted to the tribe descended from Judah the fourth son of the patriarch Jacob (Numbers). Judah was one of the twelve sons of Jacob and one of the Twelve tribes of Israel (Genesis). The Genesis 29:35  relates that Judah's mother — the matriarch Leah — named him Yehudah (i.e. "Judah") because she wanted to "praise God" for giving birth to so many sons: "She said, 'This time let me praise (odeh אודה) God (יהוה),' and named the child Judah (Yehudah יהודה)", thus combining "praise" and "God" into one new name. Thereafter Judah vouchsafes the Jewish monarchy, and the Israelite kings David and Solomon derive their lineage from Judah. In Hebrew, the name "Judah" (י ה ו [ד] ה) contains the four letters of the Tetragrammaton — the special, holy, and ineffable name of the Jewish God. The very holiness of the name of Judah attests to its importance as an alternate name for "Israelites" that it ultimately replaces.
In Jeremiah 34:9 we find the earliest reference of the word Yehudi, "Jew" being used, though the plural, Yehudim, debuts in 2 Kings 16:6 , and in 2 Chronicles 32:18. The name appears in the Bible in a verb form, in Esther 8:17  which states, "Many of the people of the land mityahadim (became Yehudim/Judeans/Jews) because the fear of the Yehudim fell on them." Also in Esther 2:5-6, we find that the name "Jew" is given to a man from the tribe of Benjamin: "There was a man a Yehudi (Judean/Jewish man) in Shushan the capital, whose name was Mordecai the son of Jair the son of Shimei the son of Kish, a Benjamite; who had been exiled from Jerusalem with the exile that was exiled with Jeconiah, king of Judah, which Nebuchadnezzar, king of Babylon, had exiled."
The Middle English word Jew derives from Old English where the word is attested as early as 1000 in various forms, such as Iudeas, Gyu, Giu, Iuu, Iuw, Iew. These terms derive from Old French giu, earlier juieu, which had elided (dropped) the letter "d" from the Middle Latin Iudaeus, which, like the Greek Ἰουδαῖος (see Ioudaioi), meant both Jews and Judeans / "of Judea". However, most other European languages retained the letter "d" in the word for Jew, and in a number of languages, including modern Hebrew and modern standard Arabic, the same word is still used to mean both Jews and Judeans / "of Judea".
From the above links there is are several points made which I will briefly re-iterate because it exemplifies exactly what many non-Yehudi (as in TEHUTI, or Dje-hud(t)i) have totally misses in this discussion/debate.
The first point point concerns matrilineal descent. I have argued before that the Biblical descent of the Patriarchs is matrilineal. Just as the descent of the Pharoanic dynasties was determined matrilineally. However, one would have to spend years (as I have) 'decoding' the Biblical genealogies to determine WHO are the reference points used to determine this matrilinearity.
Secondly, this is totally impossible if one is using the KJV and the English language to define/determine who or what is a 'Jew' (Djehudite) because the root etymoligies are 'coded language'.
For example, the Biblical genealogies, specifically as listed in the NT, vary. They give the impression that the genealogies of the Biblical Patriarchs are determine by the patrilineal line of descent. Thus, this is used by some (I won't say what 'faction') to denounce the 'Abrahamic' faiths for their 'patriarchy'.
The fact of the matter is that the distinction between the Kingdom of Judah and the Kingdom of Israel had to do with the fact that the children of 'Judah" were determined as 'Yehudites' and as distinct from 'Israel' because they were born by a woman named Tamar (hint:why do you think they later named their Kingdom in lower Kemet Ta-Mera, Ta-Mara or Ta-Meri?!).
If memory serves me correct Tamar was a Midianite woman who was the wife of one of Judah's sons, who bore Judah two sons, Pharez and Zerah, and it is from Tamar's son Pharez that the so-called House of Solomon down to Yeshua descends.
To those who claim/argue that the 'Jews' today are descendants of 'white Kazars' this is partially true.
However, study what is known as the Exilarch community (exiles) especially the 'nation' that developed in the above referenced Shushan, that is to say, SUSA or SUSIA.
Susa (Persian: شوش Shush [ʃuʃ]; Greek: Σοῦσα [ˈsuːsa]; Syriac: ܫܘܫ Shush; Old Persian Çūšā-; Biblical Hebrew שׁוּשָׁן Shushān) was an ancient city of the Elamite, Persian and Parthian empires of Iran. It is located in the lower Zagros Mountains about 250 km (160 mi) east of the Tigris River, between the Karkheh and Dez Rivers.
The modern Iranian town of Shush is located at the site of ancient Susa. Shush is the administrative capital of the Shush County of Iran's Khuzestan province. It had a population 64,960 in 2005.
In historic literature, Susa appears in the very earliest Sumerian records, e.g. in Enmerkar and the Lord of Aratta it is described as one of the places obedient to Inanna, patron deity of Uruk.
Susa is also mentioned in the Ketuvim of the Hebrew Bible by the name Shushan, mainly in Esther, but also once each in Nehemiah and Daniel. Both Daniel and Nehemiah lived in Susa during the Babylonian captivity of the 6th century BCE. Esther became queen there, and saved the Jews from genocide. A tomb presumed to be that of Daniel is located in the area, known as Shush-Daniel. The tomb is marked by an unusual white stone cone, which is neither regular nor symmetric. Many scholars believe it was at one point a Star of David. Susa is further mentioned in the Book of Jubilees (8:21 & 9:2) as one of the places within the inheritance of Shem and his eldest son Elam; and in 8:1, "Susan" is also named as the son (or daughter, in some translations) of Elam.
Greek mythology attributed the founding of Susa to king Memnon of Aethiopia, a character from Homer's Trojan War epic, the Iliad.
In urban history, Susa is one of the oldest-known settlements of the region and the world, possibly founded about 4200 BCE. Archeologists have dated the first traces of an inhabited Neolithic village to c 7000 BCE. Evidence of a painted-pottery civilization has been dated to c 5000 BCE. Its name in Elamite was written variously Ŝuŝan, Ŝuŝun, etc. The origin of the word Susa is from the local city deity Inshushinak.
Like its Chalcolithic neighbor Uruk, Susa began as a discrete settlement in the Susa I period (c 4000 BCE). These two settlements, called Acropolis (7 ha) and Apadana (6.3 ha) by archeologists, would later merge to form Susa proper (18 ha). The Apadana was enclosed by 6m thick walls of rammed earth. The founding of Susa corresponded with the abandonment of nearby villages. Potts suggests that the city may have been founded to try to reestablish the previously destroyed settlement at Chogha Mish. Susa was firmly within the Uruk cultural sphere during the Uruk period. An imitation of the entire state apparatus of Uruk, proto-writing, Cylinder seals with Sumerian motifs, and monumental architecture, is found at Susa. Susa may have been a colony of Uruk. As such, the periodization of Susa corresponds to Uruk; Early Middle and Late Susa II periods (3800–3100 BCE) correspond to Early, Middle, and Late Uruk periods.
By the middle Susa II period, the city had grown to 25 ha. Susa III (3100–2900 BCE) corresponds with Uruk III period. Ambiguous reference to Elam (Cuneiform; 𒉏 NIM) appear also in this period in Sumerian records. Susa enters history during the Early Dynastic period of Sumer. A battle between Kish and Susa is recorded in 2700 BCE.
As far as Tamar is concerned, she was also a descendant of 'Abraham' but not by his primary wife/Queen. She was a descendant of KETURAH (the Keter or K'TR of the Kaballah), the Qatara Setura, biblically described as a 'Ethiopian woman'.
Therefore, the definition of a 'Jew' as determined by matrilineal descent would be a descent of Keturah and Abraham, Tama and Judah, and their sons Pharez and Zerah.
The problem here is a one-sided POV as written in the Biblical text which focuses on the descendants of Pharez/House of David/Yeshua, while on the other side 'erasing' from the genealogical record the descendants of ZERAH who actually were never part of the Exilarch/exile community as they are the one's who fought with the Kingdom of Judah against the Babylonian conquest, but at the same time were related to the Babylonian rulers, who also descended from Keturah, back to KUSH.
Keturah was born in Kadesh, and the key here is knowings the forces at work at a specific moment in Truestory.
Djahi, Djahy or Tjahi was the Egyptian designation for southern Retenu. It ran from approximately Ashkelon to Lebanon and inland as far as Galilee. It was the watershed of the Jordan river during the Eighteenth and Nineteenth dynasty of Egypt battles with Kadesh.