Hi eqicfailninja, Take a look on Google and you will find, Federal Police officers. There are many different branches, to name a few, the United States Park Police who's jurisdiction consisted of the Federal Parks system in D.C. There is the U.S. Capital Police, Pentagon, library of Congress, the Senate, Congress, Uniform Branch of the Secret Service and The United States Department of Veterans Affairs Police, which I believe is the largest uniform division in the country with over 2,000 officers,....and on and on. I am retired from The U.S. Dept. of Veterans Affairs Police, Police series (085 GS-08 Police Supervisory Lieutenant). Each branch has jurisdiction over certain lands or property owned by the U.S. Government. Each org uses a different style of badge. (See Google) federal police badges and (federal police badge U.S. Department of Veterans Affairs). Note the Constitution does forbids the organizing of a Federal Police force.
Below are a couple badges. The first is a duty badge the second is a ceremonial badge to commentate the Presidential inauguration.
You may have gotten some answers by now, but this is what's out there in real life.