Their powers are limited to the state in which they preside
No, but they CAN be appealed to the State Court of Appeals.
General Jurisdiction courts are State Courts and Federal District courts (Including appeals and Supreme courts). Specific/Limited Jurisdictional courts are courts which can only hear certain. There are tax courts, bankruptcy courts, patent and copyright court....
A Court of Limited Jurisdiction is a court that only has authority to hear specific types of cases, usually with lower monetary limits or less severe offenses. These courts handle issues like traffic violations, small claims, and municipal ordinance violations. They do not have the authority to hear more complex or serious criminal and civil cases.
The Supreme Courts of New York are the trial courts, the lowest level courts of general jurisdiction in the New York State judiciary.
New York State designated their 62 trial courts (courts of original, general jurisdiction) "The Supreme Court of the State of New York." The State's highest appellate court is the Court of Appeals.
In the federal Judicial Branch of government, the US District Courts are the trial courts for cases of general jurisdiction. State judiciaries may also have district courts.
From their state legislature and both their state and US Consstitutions.
executive jurisdiction
In both the state and federal court systems, courts of appeals and supreme courts are those that have appellate jurisdiction over cases heard in courts of original jurisdiction (trial courts).
A difference between state and federal courts is that the federal court is limited to the types of cases listed in the Constitution, while the state courts have broad jurisdiction. Since both of the courts have jurisdiction, parties are allowed to choose to be heard by the federal or state court.
The lower state courts are courts of original jurisdiction and hear all cases within their purview and conduct jury trials. The higher state courts are not courts of original jurisdiction, only hearing cases that are referred to them by appeal of a lower court verdict or by motion. They conduct non-jury trials. These courts are the Court of Appeals and the State Supreme Court.
They do not have jurisdiction.