Your point about cards being filed as 26th Alabama is correct. However, the battalion eventually included ten companies. "A" and "C" were dispatched to Fort Donelson as you noted. The rest of the battalion remained at Tuscumbia, probably because the the other eight companies had yet to be armed. "A" and "C" eventually became "I" and "K" of the 26th Alabama Regiment.

More on this command --

On Oct 3, 1861, five companies camped at Tuscumbia, Ala, organized as the 3rd Alabama Battalion. Members of Colonel William Russell Smith’s battalion enlisted for three years or the war. Refusing to muster for that term, companies led by Captains Newton, Sanders and Reed disbanded and went home.

The original five companies were --

“A” of Fayette County, “Sipsey Guards;
“B” of Fayette County, “Dixie Boys”;
“C” of Fayette and Pickens Counties, “Luxapalila Guards”;
“D” of Marion County, “Sons of ‘76”;
“E” of Fayette County

Captain Silas Hosmer’s “Jemison Guards” reported on October 30, 1861, requesting assignment to Smith’s Battalion. By early December, previously disbanded companies had returned to camp with men willing to enroll for three years or the war. Joined by Captain Redden’s company, the battalion enlisted in Confederate service at Tuscumbia, Ala, Dec 7, 1861. This new command was sometimes mentioned as the 21st Alabama Regiment.

New companies were --

“F” of Tuscaloosa and Jefferson Counties, “Jemison Guards”;
“G” of Fayette County;
“H” of Fayette County;
“I” of Fayette and Marion Counties, “Fayette and Marion Plowboys”;
“K” of Marion County.

Led by Major John S. Garvin, Companies “A” and “C” surrendered at Fort Donelson, Tenn, Feb 16, 1862. Meanwhile, the rest of the 3rd Alabama Battalion went to Richmond, Va, reorganizing as the 26th Alabama Regiment on Mar 27, 1862. Companies “A” and “C” of the 3rd Alabama Battalion were released on exchange at Vicksburg, Miss, Sept 20, 1862, later rejoining the regiment in Virginia.