You can play a sound file of JESUS THIS IS JIMMY sung by Bobby Grove at Diana's Gospel Music. Several web sites say this recordings is from 1976.

BMI says Bobby Grove wrote JESUS THIS IS JIMMY.

I suspect this "song"--which is actually a recitation with a short sung verse at the beginning, repeated at the end--is derived from some sort of folktale or urban legend. It seems related to JIMMY BROWN THE NEWSBOY.