JOptionPane YES/No Options Confirm Dialog Box Issue

You need to look at the return value of the call to showConfirmDialog. I.E.:

int dialogResult = JOptionPane.showConfirmDialog (null, "Would You Like to Save your Previous Note First?","Warning",dialogButton);
if(dialogResult == JOptionPane.YES_OPTION){
  // Saving code here
}

You were testing against dialogButton, which you were using to set the buttons that should be displayed by the dialog, and this variable was never updated - so dialogButton would never have been anything other than JOptionPane.YES_NO_OPTION.

Per the Javadoc for showConfirmDialog:

Returns: an integer indicating the option selected by the user

Try this,

int dialogButton = JOptionPane.YES_NO_OPTION;
int dialogResult = JOptionPane.showConfirmDialog(this, "Your Message", "Title on Box", dialogButton);
if(dialogResult == 0) {
  System.out.println("Yes option");
} else {
  System.out.println("No Option");
}