Since this man was only in state militia service for six months, he cannot be found in Confederate records. If you return to the pension application and review Questions for Witness, question 7, time of service reads much more clearly. Time expired by April 1862. Georgia State Archives has incomplete records for some early six-month organizations.
http://www.georgiaarchives.org/what_do_we_have/online_records/confederate_muster_rolls/CMR_main.htm

Evidently CJB worked to assist the Confederate war effort after April 1862. He describes this as being "detailed", but in reality a man would have to be enrolled first to be detailed. CJB was of age to have been in service, but didn't enroll in a Confederate organization as stated. Since CJB was "captured" as a civilian, U S authorities did not imprison him or take him from home when Catoosa County was occupied in early September of 1863. The Yankees didn't stay long. On Sept 24, 1863, CJB sold 34 bushels of corn to Major Samuel C Muldoon of the Confederate army in Catoosa County. This record appears in the Confederate Civilians file, records of civilians doing business with the Confederate government.

The Federal army returned in late November 1863 and the area remained under U S control from that time forward. CJB signed a loyalty oath in Catoosa County 1867.

The State of Alabama would not have granted pension relief to this man because he has no record of Confederate service. The State of Georgia was much more lenient.