These men are listed under "Brite" as thier surname. You can order the service records from Missouri State Archives.
Asbury was wounded in theknee at Pleasant hill LA, on 9 April 1864.
John Richard was wounded at Pleasant Hill, erecovered and was killed at Jenkins ferry, Arkansas, 30 April 1864.
Rolla Brite is listed, but with little information.
Thomas Benton Brite is also listed, but little information. I suggest getting the Compiled Service Record for these men.