Habeas Corpus in a Texas State Appellate Court

I can't think of any exceptions to the rule that you cannot get a writ of habeas corpus in a Texas state appellate court until you have first sought one in a Texas state trial court. Cf. Ex parte Young, 418 S.W.2d 824 (Tex. Crim. App. 1967) (orig. proceeding). An appellate court does not have the capacity to make a trial record, so if you want habeas relief you have to start where a record can be made: your trial court. And remember the AEDPA clock is running from the time your trial judgment is final (not counting the times that appeals toll the finality of the judgment), and the total time you have for all your habeases is one year.
So don't start in the appellate court, bubele.

Changes in the Rules that Apply in Texas's Court of Criminal Appeals

• Effective September 1, 2011, all Petitions for Discretionary Review and all copies of the petition must be filed with the Clerk of the Court of Criminal Appeals. See TRAP Rule 68.3.
  
  Effective September 1, 2011, the opposing party has 15 days in which to file a reply to the petition with the Clerk of the Court of Criminal Appeals. See TRAP Rule 68.9.
  
  Effective September 1, 2011, the "Writ of Habeas Corpus Application Art. 11.07 form has been revised. The revised form can be found on the "Forms" link.
  
  See MISC DOCKET 11-004 [pdf] This rule supersedes Misc Docket 11-002
• New  Effective June 30, 2011, the Procedures in Death Penalty Cases involving request for Stay of Execution and related filings in Texas State and Trial Courts and the Court of Criminal Appeals has been revised.
  
  See MISC DOCKET 11-003 [pdf]. This rule supersedes Misc Docket 08-101.

The death penalty stay rule should be called The Empire Strikes Back rule. See Presiding Judge Keller breathing heavily, mechanically, "Your powers are weak, David Dow. You can't win. Though you strike me down, I shall become more powerful than you could possibly imagine." The sanctions for counsel who ignore or fail to satisfactorily meet the rule include, but are not limited to referral to the Chief Disciplinary Counsel of the State Bar of Texas, contempt of court, removal from the list of  Tex. Code Crim. Proc. Art. 11.071 list of attorneys, restitution of costs incurred by the opposing party and any other sanction allowed by law (e.g. Texas Rule of  Civil Procedure  215.2).