How can I offset a mouse pointer and where it clicks?

For example, if I wanted to make it so that to click (or hover) on something, I had to click 50 pixels to the left or below it. The motivation is that a game I'm playing incorrectly detects the mouse location in menus, so I'm hoping that offsetting the mouse manually might fix it.

Question by Jordan Morris on Super User, licensed CC BY-SA. We show a short excerpt and link to the original thread as credit.