Joseph Cresap, Co E, 1st Regiment Cav, 1st Div, MSG served 3 months 14 days. I find no other Civil War Service for him.

Virgil Cresap, native New Madrid County MO, served same unit for 6 months. He actually ends up as 2nd Srgt, Co H, 18th (Newsom's) Tennessee Cav. This unit was listed as Co H, Forrest's Alabama Cav. he was captured at Franklin TN Dec 16, 1864. He ends up at Camp Douglas, IL. Released June 10, 1865 at Point Lookout MD. At that time he listed Gibson TN as his home, 5'11'' Light complexion, Auburn hair, Light blue eyes. His service includes a report of being wounded during battle of Harrisburg, Miss. on July 13-15 1864.

Following that these were brothers we find them in 1850 in Gibson TN
Name: Joseph Cressap
[Joseph Cresap]
Gender: Male
Age: 16
Birth Year: abt 1834
Birthplace: Alabama
Home in 1850: District 2, Gibson, Tennessee, USA
Attended School: Y
Line Number: 8
Dwelling Number: 302
Family Number: 302
Household Members:
Name Age
A H Cressap 45
Nancy Cressap 42
James Cressap 18
Louisa Cressap 16
Virgil Cressap 14
Alexander Cressap 12
Joseph Cressap 16
Nelson Cressap 7

1860 census
Name: Joseph Crissop
[Joseph Cresap]
Age: 21
Birth Year: abt 1839
Gender: Male
Birth Place: Alabama
Home in 1860: District 2, Gibson, Tennessee
Post Office: South Gibson
Dwelling Number: 292
Family Number: 298

1870 finds Joseph in New Madrid County MO
Name: Joseph Cresap
Age in 1870: 29
Birth Year: abt 1841
Birthplace: Alabama
Dwelling Number: 27
Home in 1870: Big Prairie, New Madrid, Missouri
Race: White
Gender: Male
Post Office: New Madrid
Occupation: Farmer
Male Citizen over 21: Y
Inferred Spouse: Mary Cresap
Household Members:
Name Age
Joseph Cresap 29
Mary Cresap 28
Alfred Boyce 12
Olander Wysong 23
Phillip Reed 15
Edward Rannel 13

His Find a grave entry is here:
https://www.findagrave.com/memorial/30136872/joseph-a_davis-cresap