I used to work in an area where I would often see the Federal Reserve Police, due to the presence of a Federal Reserve Bank. These police officers do have police powers including the power to arrest suspects, despite the fact the Federal Reserve Bank is a private orginization.
There are other examples of private police forces with some police power, for example, many private universities have their own police force who at minimum have the right to detain suspects. The Amtrak Police is another example, however is a little more blurry since Amtrak is a federally chartered corporation.
I feel like for most of my life I was under the impression that police power solely belonged to the state, but this is obviously incorrect. I am wondering who has the authorisation to create these organisations, and how it's determined what their jurisdiction is and what police powers and protections they have.