How to display a button at the mouse position, similar to Run to cursor?

It's not quite trivial, see com.intellij.xdebugger.impl.InlayRunToCursorEditorListener

Please explain your use case, maybe there is a simpler solution.

Thank you, what I want to do is the same as Run to cursor. When the mouse moves inside the method, a button will be displayed on the left side, and clicking it will get the method name and other information

It might be possible to achieve a similar thing with Inlay Hints https://plugins.jetbrains.com/docs/intellij/inlay-hints.html in a much simpler fashion.

Thank you, I will try inlay-hints. first.

Another question, what is the name of this feature? What I want to do is to add an Action in the floating window when the mouse moves over a certain parameter.

That's a quick fix provided by inspection https://plugins.jetbrains.com/docs/intellij/code-inspections.html 

Thanks and have a nice day