Hi,Don't know if you have his enlistment record (below)or if it is for your father.
Have you written to the NPRC or the VA for any records?
Here is the NPRC site.Complete the Form 180.If they tell you his records burned, fill out the additional paperwork they send you as best you can.Give it about 6 months and then contact them to find out progress.Keep track of all contact and who you deal with and dates.
If he has passed and had a military funeral, contact the Sexton of the Cemetery and the funeral home.They should have some records.
Try the State Archives of where he enlisted and or was discharged.Also contact the County Clerk where he enlisted.
Hope some of this helps.Good Luck!!!
ARMY SERIAL NUMBER 18108963 NAME PLUMMER#JESSE#W#JR###### RESIDENCE: STATETEXAS RESIDENCE: COUNTYRUSK PLACE OF ENLISTMENTDALLAS TEXAS DATE OF ENLISTMENT DAY24 DATE OF ENLISTMENT MONTH01 DATE OF ENLISTMENT YEAR46 GRADE: ALPHA DESIGNATIONCorporal GRADE: CODECorporal BRANCH: ALPHA DESIGNATIONAir Corps BRANCH: CODEAir Corps FIELD USE AS DESIRED TERM OF ENLISTMENTEnlistment for Hawaiian Department LONGEVITY SOURCE OF ARMY PERSONNELEnlisted Reserve or Medical Administrative Corps (MAC) Officer NATIVITYTEXAS YEAR OF BIRTH19 RACE AND CITIZENSHIPWhite, citizen EDUCATION2 years of high school CIVILIAN OCCUPATIONAUTOMOTIVE MECHANIC MARITAL STATUSMarried COMPONENT OF THE ARMYRegular Army (including Officers, Nurses, Warrant Officers, and Enlisted Men) CARD NUMBER BOX NUMBER0280 FILM REEL NUMBER 3.2##