You can't associate file extensions to trigger a .jar file on Windows. The only file types you can trigger on Windows are .exe, .pif, .com, .bat, .cmd, so instead of triggering the .jar file, you can trigger a .bat file, which then launches the .jar file.
Create a y.bat file and place it next to your y.jar file and write the following code inside it:
@echo off
title y
start javaw -jar "C:\Users\SomeUsername\Desktop\y.jar" %1
You can change the title and y.jar path as you please, just remember that the path need to be the absolute path. Though the real keyword here is %1, that is the actual path, of the file you clicked.
You can get the value of any parameter using a % followed by it's numerical position on the command line. The first item passed is always %1 the second item is always %2 and so on
%* in a batch script refers to all the arguments (e.g. %1 %2 %3 %4 %5 ...%255)
Now you can simply right-click on any .abt file and press "Open With...", remember to check "Use this app for all .abt files" and then just browse for the y.bat and click "Open". Now each time you double-click a .abt file it will launch your .jar program.
Additionally I've written this post (Associate File Extension with Java Application) after writing this answer.