The US Supreme Court doesn't write any laws; that's the job of Congress, the Legislative Branch of government. The Court does interpret criminal laws to make sure they're constitutional and are applied properly, but only when the law is relevant to a case they're reviewing.
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No. The US Supreme Court is not a part of the Legislative Branch of government and plays no part in formally enacting law or in writing the text of any Act. The Court cannot draft legislation or write new laws.
However, the Court does interpret laws that are relevant to cases before the it, including parts of the Constitution that may over-ride the text of a law, and it may publish written decisions to explain its reasoning. This process of judicial review may modify or enrich the meaning of an established law. Thus the Court's written opinion can be considered part of the law-making process under the US common law system, even though it isn't the writing of a law as such.
In the United States the US Supreme Court decides if laws meet the requirements of the US Constitution.
The US Supreme Court is the highest court in the US. Each state has its own Supreme Court, but the US Supreme Court is the end of the line.
The power of judicial review allows the US Supreme Court to declare laws, policies, executive orders and US treaties that are relevant to cases before the Court unconstitutional and nullify them if they violate the principles of the US Constitution.
Unconstitutional
Ex post facto laws are specifically prohibited by the Constitution.