Baker v. Power was a United States Supreme Court case that addressed the issue of whether a state court had the authority to issue a writ of habeas corpus to a prisoner held in a federal prison. The case involved a prisoner, William Baker, who was held in a federal prison in the state of New York. Baker had been convicted of a federal crime and was serving his sentence in the federal prison. He sought a writ of habeas corpus from the state court, arguing that his conviction was unconstitutional. The Supreme Court held that the state court did not have the authority to issue a writ of habeas corpus to a prisoner held in a federal prison. The Court reasoned that the writ of habeas corpus was a federal remedy and that the state court did not have the authority to interfere with the federal government's power to imprison individuals convicted of federal crimes. The Court also noted that the writ of habeas corpus was a remedy that could only be used to challenge the legality of a prisoner's confinement, and not to challenge the legality of the conviction itself. The Court's decision in Baker v. Power established that state courts do not have the authority to issue writs of habeas corpus to prisoners held in federal prisons. The decision also established that the writ of habeas corpus is a remedy that can only be used to challenge the legality of a prisoner's confinement, and not to challenge the legality of the conviction itself.

Justice Field delivered the dissenting opinion in Baker v. Power, arguing that the court should not have granted a writ of error to review the case. He argued that it was improper for federal courts to interfere with state proceedings and noted that this decision could lead to an increase in such interference, which would be detrimental to states' rights. Furthermore, he stated that if there had been any errors made by the state court during its proceedings then they were harmless ones and did not warrant further judicial action from higher courts. Justice Field concluded his dissent by noting how important it is for each level of government—federal and state—to remain independent from one another so as not to encroach upon their respective powers or authority over certain matters.