After having jammed with neighborhood teenagers Ernie and Marvin Isley, and being added on as a brother-in-law after Isley Brothers member Rudolph married Jasper's sister Elaine, he was added to Ernie and Marvin's older brothers' band, The Isley Brothers, in 1969.
Jasper's first appearance on an Isley Brothers album was 1969's It's Our Thing. In 1973, Jasper, plus Ernie and Marvin Isley were officially added to the group. Jasper's keyboard work played a pivotal role in Isley Brothers hits such as "Fight the Power Pts. 1 & 2", "For the Love of You Pts. 1 & 2", and "Between the Sheets".
In 1984, Jasper and the younger Isleys left the Isley Brothers to form the splinter group Isley-Jasper-Isley. Jasper sung lead on the group's biggest hit, "Caravan of Love". But their tenure ended in 1987 with Jasper and Ernie Isley going into solo careers and Marvin rejoining brother Ronald in his touring band. Jasper's solo career spawned the #3 R&B hit, "Super Bad", in 1988.
After becoming a born-again Christian, Jasper released a succession of gospel albums and occasionally returned to R&B. Since the 1980s, he has recorded for Gold City Records, a record label he formed, and which is distributed by CBS Records.