It is a large piece of the copper sabot from a Confederate 3"-caliber Read shell. When that kind of shell exploded, usually the base which included the sabot stayed intact. In your case, the base blew apart, and the copper sabot also blew to pieces. You found approximately 1/3rd of the sabot's body.
Clean the rest of the dirt-encrustation off of its longer edge, and you'll see the rifling-marks (ridges) made by the cannon's barrel during firing.
Just in case you don't already know (and for any folks here who don't), here are some photos showing what the copper sabot looks like on an exploded 3"-caliber Read shell's base... and a rarely-seen intact copper Read sabot (which shows why its form is called a "ring sabot").