Here are a few bits and pieces:

Capt. Thomas H. Osborne's Scouts, after Capt. Osborne's death the unit was known as Capt. Lafayette Jenkins' Scouts.

Captain Osborne organized Osborne’s Scouts, When he fell in battle, the men elected LaFayette Jenkins Captain and the troop was thereafter known as Jenkins’ Scouts.

This company is listed in Armstrong's History of Hamilton County as an independent company, unattached to any regular organization. No muster roll, nor other record of the company was found.

Captain Osborn commanding Osborne’s Scouts, killed in action
The Confederate Soldiers of Hamilton County, Tenn.

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W. B. W. Heartsill was born in Louisville, Tennessee, on September 14, 1840, to Hiram Heartsill and Amanda Wright Heartsill. He married three times and was the father of seven children. During the Civil War, Heartsill was in the Confederate army, serving at various times as a captain, a spy, and a scout for an independent company of Tennessee scouts called Osborne’s Scouts. He also held the position of chief of police of East Tennessee at one point during the war. After the war ended, Heartsill moved to Greenwood (Sebastian County), and he remained in Arkansas for the rest of his life. He bought a farm, held positions in the Sebastian County Circuit Court, and served as a postmaster from 1885 to 1889.
http://www.encyclopediaofarkansas.net/encyclopedia/entry-detail.aspx?entryID=8312

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W. B. W. Heartsill was born in 1841 near Louisville, Tenn., southwest of Knoxville, Tenn. He served in the Army of the Confederate States of America in many positions, including captain and Chief of Police for East Tennessee. He later served as a spy and a scout with Osborne's Scouts, an independent company of Tennessee scouts. After the war ended, Heartsill moved to Arkansas. The collection consists of a handwritten manuscript entitled A Confederate Desperado by W. B. W. Heartsill. The manuscript tells the story of J. J. Cox (or Jo. J. Cox), a lieutenant in the Confederate States of America Army who deserted his post while serving with the 1st Louisiana Infantry Regiment in 1862. The narrative begins with Cox's arrest and imprisonment in the Castle Thunder Prison in Richmond, Va. The narrative details Cox's escape from prison and his many subsequent escapes from military custody. After Cox's escape from military guard in Bristol, Tenn., W. B. W. Heartsill was charged with investigating the escape and with finding Cox. Upon his recapture, Cox was sent to Heartsill's office in Bristol, and Heartsill worked to secure Cox's release as part of the general amnesty offered to Confederate deserters by Jefferson Davis on 1 August 1863. Heartsill went on to advocate on Cox's behalf in two subsequent incidents: once when Cox was arrested on a theft charge, and again when Cox was arrested on the old desertion charge. Meanwhile, Heartsill left his position as Chief of Police in March 1864 and became a scout, eventually joining Osborne's Scouts in May of that year. The narrative details various missions and engagements with Federal forces undertaken by Heartsill, sometimes accompanied by Cox. The narrative ends with the conclusion of the war and a brief account of Cox's life after the war, ending with his death in a cholera epidemic in 1866. Heartsill's opinion of Cox throughout the book was very positive; he lauded Cox's courage, good humor, and resourcefulness, and sought to disavow his reputation as a "desperate character."
http://www2.lib.unc.edu/mss/inv/h/Heartsill,W.B.W.html

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Captain George W. Kirk [3rd North Carolina Mounted Infantry] on a raid into Washington County [May/June 1864], killed Capt. Thomas H. Osborne of the Osborne Scouts, operating along the border of North Carolina.
Homegrown Yankees: Tennessee's Union Cavalry in the Civil War
By James Alex Baggett

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Heartsill’s manuscript contains a great deal of significant, realistic material about the Civil War in eastern Tennessee and western North Carolina. He is clearly intimately familiar with the area and with other locales, such as Richmond, Virginia. Even his descriptions of such far-flung places as Weldon, North Carolina, which he briefly visits, have the ring of authenticity. Among the startling revelations in the manuscript is a detailed description of Thomas H. Osborne’s scout company, known as “Osborne’s Scouts” and later “Jenkins’ Scouts.” Because this company was an irregular, nonce unit assigned as needed, no official roster of it apparently exists. Nevertheless, on pp. 168-170, Heartsill gives a detailed account of Osborne’s death in combat and a list of the names of the men who served with Osborne from time to time. A few pages later, he even recounts how Jenkins came to command the company, hence giving the unit its later name. Such detailed knowledge could hardly come from a source other than personal experience, and the manuscript is replete with such instances. Heartsill’s story closes at the end of the war, when he and his fellow scouts are paroled in Washington, Georgia.
http://www.dsloan.com/Auctions/A14/A14Web27-28.htm