It seems the lyrics posted by "GUEST" above are the original or standard lyrics, as sung by The Talley Trio and the O'Neal Twins, not the version/arrangement sung by the Third Exodus - Trinidad group.

The O'Neals' recording (vinyl) was earlier, and you can hear it here:
"Jesus Dropped The Charges" - Edgar O'Neal, piano, Edward O'Neal, lead vocal

I'm pretty sure this one is the one I saw and heard in "Say Amen, Somebody."   I definitely prefer it to the others because of its tempo, intensity, and joyful spirit!



One YouTube poster says the song was written my "Mr. Clean" and I think he's referring to Bishop Richard "Mr. Clean" White, but I can't confirm that he wrote the song.

Another source, from the '70s, refers to "the O'Neal Twins' rendition of Prof. Ronnie Felder's gospel classic 'Jesus Dropped the Charges', and it seems Felder's recording did precede Edgar and Edward O'Neal's recording, but it's still not clear whether Felder wrote the song or was simply the first one to get a lot of attention for recording it.