I need to set the position of the mouse on the screen. In some other similar question, it was suggested to use CGDisplayMoveCursorToPoint(CGDirectDisplayID display, CG
Try CGWarpMouseCursorPosition(). It doesn't require a display ID.
If you want a display ID, you can pick an element, using whatever criteria you like, from the array returned by [NSScreen screens]. Invoke -deviceDescription on that NSScreen object. From the dictionary that's returned, invoke -objectForKey: with the key @"NSScreenNumber".