Edited

"Arabian literature has its own version of prehistoric times, but it is entirely legendary." (Encyclopedia Britannica, Vol. 2:176)
"there is no historical evidence for the assertion that Abraham or Ishmael was ever in Mecca, and if there had been such a tradition it would have to be explained how all memory of the Old Semitic name Ishmael (which was not in its true Arabian form in Arabian inscriptions and written correctly with an initial consonant Y) came to be lost. The form in the Quran is taken either from Greek or Syriac sources." (Islam, Alfred Guillaume, 1956, p 26-27, 61-62)
The first positive reference to the Arabians extant occurs in an inscription of the Assyrian, Shalmaneser III, who speaks of the capture of a thousand camels from Gindibu, the Arabian, in 854 B.C. (Islam and the Arabs, Rom Landau, 1958 p 11-21)
According to Muslim tradition, God told Abraham to begin the rite of pilgrimage to Becca (now Mecca). In a rite called tawaf, Arab pilgrims from time immemorial circled the stone counterclockwise seven times and ran seven times between the two promontories in memory of Hagar's seven passages. The historicity of this Abrahamic tradition is difficult to confirm; the first verifiable reference to the Arab people occurs in an inscription of Shalmanezer III dated 853 BC. (The Joy of Sects, Peter Occhigrosso, 1996, p394-397)
"The pure Arabs are those who claim to be descended from Joktan or Qahtan, whom the present Arabs regard as their principle founder...The ‘Arabu ‘l-Musta’ribah, the mixed Arabs, claim to be descended from Ishmael.they boast as much as the Jews of being reckoned the children of Abraham. This circumstance will account for the preference with which they uniformly regard this branch of their pedigree, and for the many romantic legends they have grafted upon it...The Arabs, in their version of Ishmael’s history, have mixed a great deal of romance with the narrative of Scripture." (A Dictionary of Islam, pgs. 18-19)
"Muhammad was not informed about the family of Abraham." (Encyclopedia of Islam) I: 184. See also pages 544-546.
"There is a prevalent notion that the Arabs, both of the south and north, are descended from Ishmael; and the passage in Gen. xvi.12, "he (Ishmael) shall dwell in the presence of all his brethren," is often cited as if it were a prediction of that national independence which, upon the whole, the Arabs have maintained more than any other people. But this supposition is founded on a misconception of the original Hebrew, which runs literally, "he shall before the faces of all his brethren," i.e., (according to the idiom above explained, in which "before the face" denotes the east), the habitation of his posterity shall be "to the east" of the settlements of Abraham’s’ other descendants...These prophecies found their accomplishment in the fact of the sons of Ishmael being located, generally speaking to the east of the other descendants of Abraham, whether of Sara or of Ketuah. But the idea of the southern Arabs being of the posterity of Ishmael is entirely without foundation, and seems to have originated in the tradition invented by Arab vanity that they, as well as the Jews, are of the seed of Abraham--a vanity which, besides disfiguring and falsifying the whole history of the patriarch and his son Ishmael, has transferred the scene of it from Palestine to Mecca." (McClintock and Strong, Cyclopedia of Biblical, Theological, and Ecclesiastical Literature, (Vol. I:339)
In the Qur’an, "Gen. 21.17-21...are identified with Mecca." (The Concise Encyclopedia of Islam, p. 193). It also states that the Southern Arabs come from Qahtan, not Ishmael (p. 48).


The Arab Claim to Palestine because they are descendants of Ishmael:
By Robert Morey

The Arabs’ claim to the land of Israel rest entirely on three false assumptions:

All Arabs are the descendants of Abraham through Ishmael.
Ishmael and his descendants were included in the covenant God made with Abraham.
Since the Abrahamic convenant included the land of Israel, the Arabs have a legitimate claim to it.
Ten Historical Facts that refute these Arab claims:

According to the Torah, when Abraham left Ur of the Chaldees, he went West to what is now called Israel (Gen. 12 ff.). He became a dweller in tents in that land. It was in Israel that God made a covenant with him for the land in which he was living at that time. It was in Israel that he fathered Isaac, Ishmael, and many other sons and daughters. Isaac was the only son of Abraham chosen by God to be the heir of the covenant. Abraham took Isaac to Mt. Moriah to be offered up as a sacrifice to God.
The Torah is contradicted by Qur’an at nearly every point. According to Surah 2:119-121, Abraham and Ishmael did not dwell in tents in Israel but in the city of Mecca in Arabia. Together they rebuilt the Kabah and placed the black stone in the wall. It was Abraham who started the tradition of an annual pilgrimage to Mecca, throwing stones at the devil, etc. Abraham took Ishmael (not Isaac) to nearby Mt. Mina to offer as a sacrifice to God.
Ishmael’s twelve sons were named Nebaioth, Kedar, Adbeel, Mibsam, Mishma, Dumah, Massa, Hadad, Tema, Jetur, Naphish, and Kedemah. (Gen. 12:11-16) They intermarried with the local population in North Arabia and produced several nomadic tribes know as the "Ishmaelites."
It was prophesied in the Torah that Ishmael and his family would "live to the East of all his brothers." (Gen. 16:12) "And they settled from Havilah to Shur which is east of Egypt as one goes toward Assyria." (Gen 25:18) This broad area is the desert section East of Egypt in Northern Arabia toward the kingdom of the Assyrians.
The Ishmaelites are mentioned as a distinct tribe in the Assyrian records. They later intermarried with and were absorbed by the Midianites and other local tribes. In Gen. 37:25-28; 39:1, the Ishmaelites are called the Midianites and in Judges 8:22-24 cf. 7:1f, the Midianites are called the Ishmaelites. The identification cannot be made any stronger.
Arabia was already populated by the descendants of Cush and Shem long before Abraham or Ishmael were born (Gen. 10:7). Their cities and temples have been well documented by archeologists.
If all the Arab people descended from Ishmael as Muhammad claimed, where did all the original Arabs go? What happened to them? Who did Ishmael marry if the Arabs did not already exist? If Arabia was unpopulated, who built Mecca? Since he lived there, obviously it existed before he was born. The facts speak for themselves. The Arab people existed before, during, and after Ishmael moved started roaming the wilderness of North Arabia.
The descendants of Ishmael were scattered in Northern Arabia from the wilderness of Shur to the ancient city of Havilah. They were absorbed by the local tribes such as the Midianites (Gen. 37:25-28; 39:1; Judges 8:24). There is no historical or archeological evidence that Ishmael went south to Mecca and became the "Father" of the Arab race. Some modern Arab scholars admit that before Muhammad, Qahtan was said to be the "Father" of the Arab people, not Ishmael.
The Abrahamic Covenant was given only to Isaac and to his descendants. Ishmael and the other sons of Abraham were explicitly excluded by God from having any part of the covenant made with Abraham. (Gen. 18:18-21)
Therefore the descendants of Ishmael and the other sons of Abraham do not have any claim to the land of Israel because they are not included in the covenant God made with Abraham. Only the Jews have any claim to the land of Israel.
The Islamic Claim to Palestine because they are descendants of Ishmael:

Muslims like to claim that Islam gave them the right to claim the land of Israel as their own. This claim rests upon two false assumptions:

All Arabs are the descendants of Ishmael;
Muhammad went to Jerusalem.
Three Historical Facts that refute these Islamic claims:

The first assumption has already been proven false. The Arab people are not all the descendants of Ishmael and hence they are not the heirs of the Patriarchs, the prophets, the Scriptures or the land of Israel.
The claim that Muhammad went to Jerusalem is false. According to the Qur’an and the Hadith, Muhammad had a dream in the middle of the night in which he traveled through the sky, visited seven heavens, met great people like Jesus, and visited the Jerusalem. Since this was only a dream, he was never actually in Jerusalem. The Mosque on the temple site in Jerusalem is a hoax built on the lie that Muhammad stood on the site.
Nowhere in the Qur’an does it state that Ishmael is the progenitor of the Arab race. Since it is not taught in the Qur’an, it cannot be a true Islamic belief.
Conclusion

The Arab people are not the children of Ishmael. Even if they were, they would still have no claim to Israel because Ishmael was excluded by God Himself from having any part in the covenant made with Abraham. Isaac was the only heir of the Abrahamic covenant. Thus the Arabs as a people have no claim to the land of Israel.

The Muslims have no claim to the land of Israel either. Muhammad never went to Jerusalem except in a dream. The only ones with a spiritual and biblical claim to the land of Israel are the descendants of Isaac, the Jews.

Other references:

The Encyclopedia of Religion, Vol. 7, pg. 296 where the connection between the Midianites and the Ishmaelites is noted.
The Shorter Encyclopedia of Islam, pgs. 178-179.
A Popular Dictionary of Islam, p. 127.
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