The Constitution sets minimum age, citizenship, and residency requirements for federal offices, and bars Congress from adding more qualifications beyond what Article I and Article II specify. House members must be at least 25 years old, U.S. citizens for seven years, and live in their state when elected. Senators need to be 30, citizens for nine years, and state residents. The president must be a natural-born citizen, at least 35, and a U.S. resident for 14 years.
The Framers made Senate qualifications more rigorous than the House because they wanted the Senate to be a more deliberative, experienced body. In U.S. Term Limits, Inc. v. Thornton (1995), the Supreme Court ruled states can't add term limits or other qualifications to federal offices—only a constitutional amendment can change these requirements.