That certainly carries a bit of weight.
While it does narrow it down to possible six chapters about those three countries in that Register: 10, 11, 12, 13, 14, and 15. Q specifically says “chapters”, so at least two of them are his.
The timing is also strong. The register is for 1827/1828/1829, and his letter is dated the following year, 1830.
Is there more?
I mean, its solid to me. I’m convinced. But that won’t convince everybody. There is a shadow of a doubt that remains. Did he only write two or three of those six? Five of the six?
Unfortunately, with conservatives not willing to go into the historical field over the decades this is the situation we’re forced to deal with and be trapped in. We’ve let the progressives win. I’m hoping the work I do will help lay the groundwork to change that in the future, but we’re talking decades here. First we have to get rid of the unwillingness and that’s not going away any time soon.
Is there more?
There is some more that may be useful to your research. For what it is worth, here it is.
JQA Diary, volume 36
5 March 1830
5. V. Friday.—Sun rose 6:Clements.
Bartlett
Wool—General
White Joseph MReturned from my walk to see the Sun rise. Mr Clements and Mr Bartlett are workmen upon the Canal, one from Maine, the other from New-Hampshire who came to see me, merely from curiosity—Clements said he was going to the State of Ohio, and Bartlett that he should return home. General Wool, was ordered here as a member of the Court-Martial, now sitting for the trial of Coll Roger Jones the Adjutant General; but he told me he had come too late—Mr White of Florida, called for his wife’s Album; but I had neglected to write in it as she had requested; and was obliged to ask him to call again—We received the American Quarterly Review, in which there is an Article upon Russia and Turkey, and one upon Mohammedan History, both full of information, upon the subject which now occupies me—The first is a historical review of the eight Wars between Russia and Turkey which preceded the last. There is in this review, reference made to at least thirty authors, French, English, German, Italian and Russian, to scarcely one of which I can have access—The writer appears to be familiar with them all—Karamsin’s History of Russia, and Von Hammer’s German History of the Ottoman Empire are works new to me—He says that Von Hammer is the most eminent Oriental Scholar that has ever appeared in Germany, and except Sylvestre de Sacy, has no rival in Europe—There is a short abstract of the causes and issue of every War between Russia and Turkey, from the first in 1569. to the eighth from 1807 to 1812—an animated account of the establishment of the House of Romanoff upon the throne of the Czars, in 1613. a rapid sketch of the character of Alexis, father of Peter the Great; and some dramatic touches of the History of Peter himself. A Satirical attack upon the Austrian Government for ingratitude to Prince Eugene, whom he calls the modest and valiant Eugene. This person is no favourite of mine—He was a Coriolanus—A Frenchman; born a Subject of Louis 14. bred to the Church, and after being in Ecclesiastical orders; deserting his Country, and going over to the Sovereign of Austria, because he could not obtain of the Government of Louis 14 a Commission as Commander of a Troop of horse. For this he invaded his Country and fought numbers of bloody battles against her— He went over to England too to raise a riot against the Tories, with the Duke of Malborough— There are other things too much against this same Prince in despite of his high reputation—The Article on Mahommed is not equal to the first, but has much information—The author Professes acquaintance with the Oriental Languages, and gives a severe criticism upon the Koran.
While he speaks here of the author in the third person, he may just have wanted to keep his authorship anonymous. He was not long out of office as President.
https://www.christies.com/en/lot/lot-4606529
ADAMS, John Quincy. Autograph letter signed ("J. Q. Adams") to Joseph Blunt, editor of the American Annual Register, Washington, 9 April 1830. 2 full pages, 4to. In very fine condition.
A previous diary entry mentioned corrections to the unsigned chapters sent to Blunt. This details those corrections.
https://www.jstor.org/stable/40371517
It was with a great deal of pride that Robert Walsh, who edited simultaneously the Philadelphia National Gazette and Literary Register and the American Quarterly Review between 1827 and 1836, revealed in his newspaper the following distinguished writers who had contributed to his quarterly prior to 1835:Messrs. John Q. Adams, ....
Cites to the below for a Robert Walsh editorial where Walsh named various authors of unsigned matter that was published in the AQR. It is not clear if Walsh listed the specific articles by specific author, or merely related that they had contributed material. I have not found that editorial page. Of the listed authors, John Q. Adams is the first. If the editorial can be found, it may provide the provenance you seek.
The National Gazette and Literary Register, January 28, 1835, p. 2, col. 2. editorial by Robert Walsh