What power does the Constitution give to the Supreme Court?
The framers placed the judiciary branch in article 3, after the more important congressional and executive branches.
The Supreme Court is tasked to interpret the text and meaning of the Constitution.
Justices creating new clauses or meanings to change the Constitution are usurping power that belong to the Congress and the States to change the Constitution via amendments.
In general, the judicial power and authority of the Supreme Court extends to all Cases arising under the Constitution. But the courts appellate jurisdiction authority is subject to regulation by the Congress. It is possible for Congress to remove some cases from federal court purview.
US Constitution - Article 3 - The Judicial Branch
Section 1 - Judicial Powers
The judicial Power of the United States, shall be vested in one supreme Court, and in such inferior Courts as the Congress may from time to time ordain and establish. The Judges, both of the supreme and inferior Courts, shall hold their Offices during good Behavior, and shall, at stated Times, receive for their Services a Compensation which shall not be diminished during their Continuance in Office.
Section 2 - Trial by Jury, Original Jurisdiction, Jury Trials
The judicial Power shall extend
to all Cases, in Law and Equity,
arising under this Constitution,
the Laws of the United States,
and Treaties made, or which shall be made, under their Authority;
to all Cases affecting Ambassadors, other public Ministers and Consuls;
to all Cases of admiralty and maritime Jurisdiction;
to Controversies to which the United States shall be a Party;
between two or more States;
between a State and Citizens of another State;
between Citizens of different States;
between Citizens of the same State claiming Lands under Grants of different States,
and between a State, or the Citizens thereof, and foreign States, Citizens or Subjects. (This section is modified by the 11th Amendment)
11th Amendment - Judicial Limits
The Judicial power of the United States shall not be construed to extend to any suit in law or equity, commenced or prosecuted against one of the United States; by Citizens of another State, or by Citizens or Subjects of any Foreign State.
In all Cases affecting Ambassadors, other public Ministers and Consuls, and those in which a State shall be Party, the supreme Court shall have original Jurisdiction.
In all the other Cases before mentioned, the supreme Court shall have appellate Jurisdiction, both as to Law and Fact, with such Exceptions, and under such Regulations as the Congress shall make.
The Trial of all Crimes, except in Cases of Impeachment, shall be by Jury; and such Trial shall be held in the State where the said Crimes shall have been committed; but when not committed within any State, the Trial shall be at such Place or Places as the Congress may by Law have directed.
Section 3 - Treason
Treason against the United States, shall consist only in levying War against them, or in adhering to their Enemies, giving them Aid and Comfort. No Person shall be convicted of Treason unless on the Testimony of two Witnesses to the same overt Act, or on Confession in open Court.
The Congress shall have power to declare the Punishment of Treason, but no Attainder of Treason shall work Corruption of Blood, or Forfeiture except during the Life of the Person attainted.