What caused the Maybury vs Madison case ?

The case arose out of the fierce political rivalry between the outgoing Federalist Administration and its Democratic-Republican opponents. Thomas Jefferson, the Democratic-Republican candidate for President, had defeated the incumbent John Adams in the 1800 election. Yet as Inauguration Day would not take place until March of the following year, Adams remained as President, with all the powers that the role entailed.
One of the most important of those powers was that of judicial appointment. Adams was worried that the incoming administration would undo his entire political program. So in the dying days of his presidency he made a number of appointments to the Federal bench, hoping to pack the courts with his political supporters in order to stymie any attempts by the next administration to undermine his legacy.
One of the men due to be appointed was William Marbury. Yet he was denied his appointment at the 11th hour by the new Secretary of State, James Madison, who had not delivered his formal commission on time before President Jefferson's inauguration. In court, the government argued that as the commission had not been delivered on time, Marbury was not entitled to take up his new position. For his part, Marbury was aggrieved that he had been denied a judicial role given to him by the duly constituted legal authority, i.e. President Adams.
In a landmark ruling, the Supreme Court, consisting largely of Federalists such as Chief Justice John Marshall, held that Marbury was not entitled to his appointment, even though Madison's failure to deliver his commission was illegal. The Court's rationale for handing down the decision was purely political. Marshall knew that if the Court ruled in Marbury's favor it would generate a bitter conflict with the Jefferson Administration, which might well result in the Court's having its wings clipped by the President and his supporters, who now had a majority in Congress.
More importantly, the Court also invalidated the law that had given it jurisdiction in the Marbury case. Ironically, then, the Supreme Court struck down a law that had given it more power. Yet in doing so, it arrogated to itself yet greater power: the power of judicial review. The Court had given to the Jefferson Administration with one hand and taken with the other. From that day on, the Supreme Court would have the right to strike down laws as unconstitutional.
https://www.history.com/this-day-in-history/marbury-v-madison-establishes-judicial-review

https://www.oyez.org/cases/1789-1850/5us137