Branch v. Jesup 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 federal custody. The case arose when a prisoner, William Branch, was arrested and held in federal custody in Georgia. Branch sought a writ of habeas corpus from the state court, claiming that his arrest and detention were illegal. The state court granted the writ, and the federal government appealed the decision to the Supreme Court. 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 federal custody. The Court reasoned that the writ of habeas corpus was a federal prerogative, and that the state court did not have the authority to interfere with the federal government's power to detain a prisoner. The Court also noted that the writ of habeas corpus was a fundamental right, and that the federal government had the exclusive power to protect that right. In conclusion, 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 federal custody. The Court reasoned that the writ of habeas corpus was a federal prerogative, and that the state court did not have the authority to interfere with the federal government's power to detain a prisoner. The Court also noted that the writ of habeas corpus was a fundamental right, and that the federal government had the exclusive power to protect that right.

Justice Field delivered the dissenting opinion in the case of Branch v. Jesup, arguing that a state court's decision should not be overturned by federal courts unless it is clearly wrong or unconstitutional. He argued that because there was no clear error on behalf of the state court, and since its decision did not violate any constitutional rights, then it should stand as valid law. Furthermore, he argued that even if an error had been made by the state court in interpreting a statute or common law principle, this would still not give rise to jurisdiction for a federal court to overturn such decisions; rather they must remain within their own sphere of authority and respect those decisions made by other courts. In conclusion Justice Field believed that due deference should have been given to the ruling of the State Court and thus his dissent from majority opinion which held otherwise.