In the 1870 census Albert T. Slusher was listed as 21, with the family of Solomon and Permilia Slusher:

1870 census of Floyd Co., Virginia, Indian Valley & Burks Fork townships, enumerated 1 Sep, lists on p. 41 as family #283/267:
Slusher, Solomon, 74, miller; Permilda, 77; Albert T., 21, farm laborer. All born in Virginia.

He is too young to be their son (Permilia would have been 56 when he was born), suggesting he may a grandson. However, the only known sons of Solomon and Permilia Slusher are Allen, William and Solomon, and all of them appear in the 1860 census with no son who fits to be Albert. (The closest possibilities are Thomas age 10 son of Allen, and Amos T. age 6 son of William, but both of those individuals also appear in 1870 and/or 1880, making it impossible for them to be the same as Albert.)

Indeed, I was not able to find any Albert Slusher approximately 10 to 12 in 1860 in all of Virginia, nor any Slusher male of the right age with an initial T in Floyd Co who did not appear independently in 1870.

The only possibility I found is that in the 1860 census, next door to Solomon Slusher Jr. (Solomon and Permilia’s son), and just four households away from Solomon and Permilia (at #1138/1061), was an Albert T. Sutphin, age 11, with the family of Milton W. Sutphin and his wife Celia, who was Solomon and Permilia’s daughter:

1860 census of Floyd Co., Virginia, Greasy Creek P.O., enumerated 13 Aug, lists on p. 157 as family #1134/1157:
Milton W. Sutphin, 41, farmer; Celia, 30; Albert T., 11. All born in Virginia.

There is no Albert Sutphin listed in the 1870 census. Furthermore, Floyd Co., marriage records list the marriage of Milton Sutphin and Celia Slusher on 26 Nov 1857, less than three years before the above census reading. I am therefore concluding that Albert T. Slusher was a child of Celia Slusher before she was married, and was incorrectly listed as a Sutphin in the 1860 census.

He does not appear in the 1850 census, and in 1850 Celia is listed with her parents, and no child. So it is possible that all the later records are incorrect, and he was really born in June of 1850 instead of 1849. (The census is supposed to record only persons alive on June 1, regardless of what date the enumerator visits the household.)

1880 census of Floyd Co., Virginia, Indian Valley district, enumerated 5 June, lists on pp. 13-14 as family #114/115:
Slusher, Albert T., 30, farmer; Martha J., wife, 29; Henry H., son, 8; Permelia E., 5; William T., 3; James A., 1; Martha J., 0, born May. (This family is split between pages, and the relationships are blank on the continuation.)

1900 census of Floyd Co., Virginia, Burks Fork district, enumerated 22 June, lists on p. 8A as family #144:
Slusher, Albert, 50, b. June 1849, farmer; Martha J., wife, 49, b. July 1850, married 29 years, mother of 13 children, 11 living; Martha J., dau, 20, b. May 1880; Elen A., dau, 17, b. July 1882; Edward S., son, 16, b. Mar 1884; Benjamin F., son, 14, b. Apr 1886; Giles M., son, 11, b. Apr 1889; Ether M., dau, 9, b. Jan 1891; Ellis L., son, 5, b. Sep 1894; John W., son, 2, b. June 1897; Sutphin, Celia, mother, 70, b. Apr 1830, widowed, mother of 1 child, 1 living. All born Va Va Va.

1910 census of Floyd Co., Virginia, Court House district, enumerated 4 May, lists on p. 7A as family #121/125:
Slusher, Albert Tell, 60, house painter; Martha J., wife, 59, first marriage for both, married 39 years, mother of 13 children, 11 living; Ether M., dau, 19; Ellis L., son, 15; John W., son, 12; Slusher, Celia, mother, 80, widowed, mother of 1 child, 1 living. All born Va Va Va.

1920 census of Floyd Co., Virginia, Courth House district, enumerated 20 Jan, lists on p. 8A as family #151/152:
Slusher, Albert T., 20, house painter, b. Va N.C. Va; Marth J., wife, 69; Ellis L., son, 25; Sutphin, Celia, mother, 89, widowed. All except Albert born Va Va Va.