My assumption is that it is not a fossil, but there really is no way I can confirm that from a photo. There’s no scale bar in your photo, but it appears that the bone is too small to be from a hominid (human or neanderthal).
I’m sorry I don’t really understand what you are asking. I don’t know what “authorities” you are worried about, but I cannot tell you about the legality of what you found from any photo or video. You may have to bring it to a museum and speak to someone in person.
Hi @Sonya-Babcock, if you feel you have encountered a modern human grave site (i.e. finding associated bones), the best thing to do is contact local authorities and alert them to the location of the grave. However, due to the size and shape of this bone, I suspect this is just a modern animal bone and that there is nothing to worry about.