Well, beginning from a position of knowing nothing about the unit, I can at least say there was an independent company, Logan's Company, which was raised in Coosa County. The Alabama Archives (Montgomery) has a folder for this organization.

Your company, Logan's Mounted Reserves, was commanded by Capt. Ellis Logan (according to the muster roll in Broadfoot), and I assume that the two companies are one and the same.

There are a couple of references on the web to the unit. Here is information posted on Capt. Ellis Logan:

"Ellis Logan was born on January 30, 1815, in Blount County, Tennessee to Henry Logan and Martha George.... Ellis Logan enlisted as a Captain in Co. H of the 13th Alabama Regiment on July 2, 1861, in Coosa County, Alabama. At the time of his enlistment, he resided in Rockford, [was] 46 years old, married, and the sheriff of Coosa County. He was at the Siege of Yorktown, Virginia, from April 5, 1862 to May 3, 1862.... After arriving in Richmond, Ellis Logan resigned from the Confederate Army after serving only eleven months of active duty, due to ill health. After returning to Coosa County, he began farming as a way of making a living for his family. On July 25, 1864, Ellis Logan organized a local denfense company of mounted reserves in Rockford, Coosa County, Alabama, called Logan's Mounted Company in which he served as a Capatain.... Ellis Logan died on September 4, 1898, at Davis Creek, Fayette County, Alabama. He is buried at Rose Hill Cemetery in Fayette County.... Ellis Logan lived to be 83 years old. During his lifetime, he [saw] the United States at its best and at its worse. He was married three times and raised twenty four children."