If he enlisted in Kentucky then the only two matches I found were "Joseph Patterson, 15th Regiment Slaughter's Kentucky Militia" and "Joseph Patterson, 1st Regiment Light Dragoons (cavalry), Simrall's Kentucky Volunteers."
These regiments were raised locally, therefore members of a militia regiment were generally from the same area. Find out exactly where your ancestor lived then study his neighbors. Look at the muster rolls for these regiments and compare the names. Rule out the other "Joseph Pattersons" based on their locations. Likewise, it is unlikely that your ancestor would have joined a regiment raised say, 100 miles from his home.
He has a snappy-looking tombstone. He died Jan 2, 1863 in Montgomery Co., Indiana. Maybe his obituary mentions his military service.