After the Constitutional Convention of 1787 in Philadelphia, two positions towards the proposed Constitution raised, the Federalists were in favor of the proposed Constitution and were advocates for a strong federal government, hence their name. The Anti-federalists feared that a strong federal government could lead to an abuse of power, and that the states' sovereignty and the people's rights could be in jeopardy.
In order to approve the Constitution, a ratification process was needed (nine states in favor) and the Federalists (Alexander Hamilton, James Madison and John Jay) wrote the Federalist papers under the name of Publius, to persuade the state of New York, and the Anti-Federalists exposed the reasons why a Bill of Rights was needed. The addition of the Bill of Rights drafted by James Madison and adapted as the first ten amendments of the Constitution was how the Federalists and Anti-Federalists fixed their issue.