Petitioner Adam Davis, Jr., brings a fourth petition to reinvest jurisdiction in the trial court to file a petition for writ of error coram nobis in the trial court in his criminal case. This court dismissed or denied his first three such petitions. Davis v. State , 2017 Ark. 74, 511 S.W.3d 847 (per curiam); Davis v. State , 2016 Ark. 296, 498 S.W.3d 279 (per curiam); Davis v. State , 2016 Ark. 69, 2016 WL 675435 (per curiam). Additionally, Davis filed a motion to proceed in forma pauperis, a motion for appointment of counsel, and a motion that he be permitted to file a response to the State's response to his petition in which he argues that recent precedent supports his claims for relief.
In the petition, Davis contends that he was not competent to stand trial; that the trial court did not meet its obligation under Ake v. Oklahoma , 470 U.S. 68, 105 S.Ct. 1087, 84 L.Ed.2d 53 (1985), to provide him with a mental-health expert to assist in his defense; that the State violated Brady v. Maryland , 373 U.S. 83, 83 S.Ct. 1194, 10 L.Ed.2d 215 (1963), by not disclosing all evidence favorable to the defense; that the evidence was insufficient to establish that he acted with deliberation and premeditation when he committed the offenses of which he was convicted; and that the trial court erred in declining a jury instruction favorable to his claim of mental disease or defect and in denying the jury access to significant information concerning his mental state. We find that the allegations are largely a repetition of claims already raised in his prior petitions, and to the degree that Davis has enlarged on the claims, the claims are without merit. For this reason, the petition is dismissed as an abuse of the writ. Davis's motion to proceed in forma pauperis, motion for appointment of counsel, and motion to be permitted to file a response to the State's response are moot.
I. Nature of the Writ
The petition for leave to proceed in the trial court is necessary because the trial court can entertain a petition for writ of error coram nobis after a judgment has been affirmed on appeal only after we grant permission. Newman v. State , 2009 Ark. 539, 354 S.W.3d 61. A writ of error coram nobis is an extraordinarily rare remedy. State v. Larimore , 341 Ark. 397, 17 S.W.3d 87 (2000). Coram nobis proceedings are attended by a strong presumption that the judgment of conviction is valid. Green v. State , 2016 Ark. 386, 502 S.W.3d 524 ; Westerman v. State , 2015 Ark. 69, 456 S.W.3d 374 ; Roberts v. State , 2013 Ark. 56, 425 S.W.3d 771. The function of the writ is to secure relief from a judgment rendered while there existed some fact that would have prevented its rendition if it had been known to the trial court and which, through no negligence or fault of the defendant, was not brought forward before rendition of the judgment. Newman , 2009 Ark. 539, 354 S.W.3d 61. The petitioner has the burden of demonstrating a fundamental error of fact extrinsic to the record.
*114Roberts , 2013 Ark. 56, 425 S.W.3d 771. It is the petitioner's burden to show that a writ of error coram nobis is warranted. This burden is a heavy one because a writ of error coram nobis is an extraordinarily rare remedy. Jackson v. State , 2017 Ark. 195, 520 S.W.3d 242.
II. Grounds for the Writ
The writ is allowed only under compelling circumstances to achieve justice and to address errors of the most fundamental nature. Id. A writ of error coram nobis is available for addressing certain errors that are found in one of four categories: (1) insanity at the time of trial, (2) a coerced guilty plea, (3) material evidence withheld by the prosecutor, or (4) a third-party confession to the crime during the time between conviction and appeal. Howard v. State , 2012 Ark. 177, 403 S.W.3d 38. This court will grant permission to proceed with a petition for the writ only when it appears that, looking to the reasonableness of the allegations of the proposed petition and the existence of the probability of the truth of those allegations, the proposed attack on the judgment is meritorious. Isom v. State , 2015 Ark. 225, 462 S.W.3d 662.
III. Background
In 2008, a jury found Davis guilty of capital murder, attempted first-degree murder, and two counts of use of a firearm in the commission of a felony. Consecutive sentences of life imprisonment without parole and a total of 720 months' imprisonment were imposed. We affirmed. Davis v. State , 2009 Ark. 478, 348 S.W.3d 553.
IV. Repetition of Claims for the Writ
The grounds raised by Davis in this fourth petition are issues already raised in his three prior petitions for writ of error coram nobis. Reassertion of the same claims without sufficient facts to distinguish the claims from those raised in a previous coram nobis petition is an abuse of the writ and subjects the petition to dismissal. Jackson , 2017 Ark. 195, 520 S.W.3d 242 ; see also United States v. Camacho-Bordes , 94 F.3d 1168 (8th Cir. 1996) (holding that res judicata did not apply to bar a second petition for writ of error coram nobis, but abuse-of-writ doctrine was applied to subsume res judicata). Due process does not require this court to entertain an unlimited number of petitions to reinvest jurisdiction in the trial court to consider a petition for writ of error coram nobis in a particular case. This court has the discretion to determine whether the renewal of a petitioner's application for the writ will be permitted to go forward even if there are additional facts in support of repetitive grounds. Chatmon v. State , 2017 Ark. 229, 2017 WL 3300517.
In his first petition, Davis argued that the trial court made several errors in its rulings and that he was denied due process because the court did not allow into evidence all the evidence he desired to bring forth to the jury. The same allegation is raised again in this fourth petition with the addition of new claims of trial error, but a claim of trial error is not a ground for the writ. By its very nature, a question concerning a trial court's ruling could have been settled in the trial court and on the record on direct appeal. Accordingly, the allegation that the trial court made some mistake in its rulings, including rulings concerning the admissibility of evidence, is not within the purview of a coram nobis proceeding. Mason v. State , 2014 Ark. 288, 436 S.W.3d 469. The writ will not lie to retry the defendant or to reexamine the strength of the evidence adduced at trial. Carner v. State , 2018 Ark. 20, 535 S.W.3d 634.
With respect to Davis's assertion that he was incompetent, which appears *115to encompass his mental state both at the time of the offenses and at the time of trial, the claims are essentially the same as those raised in his earlier petitions. Merely restating an allegation raised in a prior coram nobis petition does not automatically provide grounds for a successive petition for the writ. Chatmon , 2017 Ark. 229. Davis has expanded on the claim of incompetence by contending that he should have been provided with a mental-health expert to assist the defense under Ake and other cases and that his mental evaluation should have been conducted at the Arkansas State Hospital rather than at another facility. These additional allegations do not constitute a showing of evidence extrinsic to the record that could not have been argued at trial. The writ functions to correct mistakes of fact, not mistakes of law. Ridgeway v. State , 239 Ark. 377, 389 S.W.2d 617 (1965).
Davis argued at trial that his intent or state of mind was the central issue in whether he was guilty of the offenses and that the State failed to prove that he acted with the requisite mental state for each offense. Defense counsel sought, and was denied, instructions on the lesser-included offenses of second-degree murder and manslaughter with extreme emotional disturbance. The crux of Davis's grounds for the writ in all of his petitions-including the one now under consideration-with respect to the evidence adduced at trial, as well as the evidence he argued could have been adduced, was that there was information available that he wanted the jury to hear and was not brought out. The argument, as such, does not satisfy any ground for granting the writ because Davis does not argue that there was any evidence extrinsic to the record that was hidden from the defense or that was unknown at the time of trial. Larimore v. State , 327 Ark. 271, 938 S.W.2d 818 (1997). Neither Davis's dissatisfaction with the trial court's rulings concerning his competence nor his dissatisfaction with the evidence presented to the jury constitutes a showing of extrinsic evidence that would have produced a different verdict had it been known at trial. See Cloird v. State , 357 Ark. 446, 182 S.W.3d 477 (2004).
Davis continues to fail to offer facts sufficient to warrant granting leave to proceed in the trial court for the writ. See Jackson , 2017 Ark. 195, at 7, 520 S.W.3d 242, 247 (The addition of new factual allegations surrounding an issue raised in a prior petition was not sufficient to distinguish the claims in the latest petition from the claims in prior petitions in that the allegations involved matters that were known or could have been discovered at the time of trial and otherwise failed to establish that material evidence had been withheld by the prosecution.). The application for coram nobis relief must make full disclosure of specific facts relied on as the basis for the writ. Martinez-Marmol v. State , 2018 Ark. 145, 544 S.W.3d 49. Because those few additional facts that Davis offers are not sufficient to support his claims, this fourth petition, as with the third petition, is an abuse of the writ and subject to dismissal for that reason.
Davis further invokes Brady , 373 U.S. 83, 83 S.Ct. 1194, 10 L.Ed.2d 215, as a ground for the writ and claims that the State should have produced for the jury all available information pertaining to his mental health. The mere fact that a petitioner alleges a Brady violation is not sufficient to provide a basis for the writ. Wallace v. State , 2018 Ark. 164, 545 S.W.3d 767 ; see also Penn v. State , 282 Ark. 571, 670 S.W.2d 426 (1984) (a mere naked allegation that a constitutional right has been invaded will not suffice to warrant coram nobis relief). To establish a Brady violation, the petitioner must satisfy *116three elements: (1) the evidence at issue must be favorable to the accused, either because it is exculpatory or because it is impeaching; (2) that evidence must have been suppressed by the State, either willfully or inadvertently; (3) prejudice must have ensued. Howard , 2012 Ark. 177, 403 S.W.3d 38. Here, Davis offers no proof that the State suppressed any specific evidence pertaining to his competence. Mosley v. State , 2018 Ark. 152, 544 S.W.3d 55 (holding that a Brady violation occurs if the defense was prejudiced because the State wrongfully withheld evidence from the defense prior to trial).
Petition dismissed; motions moot.