I use the following method to make an application remain on top of other windows in Qt:
SetWindowPos ( (HWND)winId(), HWND_TOPMOST, window_top_pos, window_left_pos, window_width, window_height, SWP_SHOWWINDOW );
Note that window_top_pos, window_left_pos, window_width and window_height are variables and you can replace them with your own.
Please be aware that this is a Win32 API function so it won’t work in Linux or MAC.
Don’t forget to add the include file to your code.
And add the required library to your .PRO file.
LIBS += -luser32