How can I trim off the corner of this stud?
Maybe there was a drywall patch and this is a back brace?

From your description, it appears that trimming this piece will do no harm (and a lot of good).  

The easiest method is to use a multitool.



There are numerous good brands, and they come with a variety of blades and other attachments.

These versatile tools make cutting, sanding grinding in tight spaces much easier. They vibrate their blades and other attachments very rapidly in short strokes from side to side. If you buy one, you will be surprised how often is it the easiest way to do a job (e.g., trimming the bottom of door jambs to insert engineered floor boards).