Q: Keyboard shortcut for window snapping

You could try Better Snap Tool.

https://itunes.apple.com/au/app/bettersnaptool/id417375580?mt=12

I haven't used it myself, but the description appears to describe the functionality you are requesting.

It is only $3. That is very close to free.

BetterTouchTool is still free and has most of the snap features, but it will be going to a paid model in a month or 2.  But you get a great tool for enhancing your track pad experience, and hotkey mapping thrown in.

Otherwise there are some other snap tools out there.  You could Goggle for them.

The only thing El Capitan has is the vertical split screen of 2 windows by picking the first window and doing a click and hold on the green button, then select the 2nd window to share the other half of the screen.  Otherwise window snapping is not in the OS X toolbox.