In the quite normal situation, after a new application is downloaded from the Internet and is run for the first time, a warning message is shown: " * is an application downloaded from the Internet. Are you sure you want to open it?". Actually, after you answer it with a yes. this message shouldn't appear anymore in the following starting up the application. This is the normal case!!!
Let's start a strange one: the warm warning message consistently appear in every times' start up process of some specific application. I believe that this is caused by an inappropriate installation of the application. The main point is that how to get ride of the message!!!
xattr -d -r com.apple.quarantine /Path/to/application/
this should be run in a super user mode.
reference: osxdaily.com/2010/09/12/disable-application-download-from-the-internet-message-in-mac-os-x/