Co-written and first recorded by Don Covay & the Goodtimers (1960).
Hit version by Chubby Checker (US #1/R&B #1 1960).
From the wiki: “‘Pony Time’ was written by Don Covay and John Berry (a member of Covay’s earlier vocal group, the Rainbows), and originally recorded in 1960 by Covay with his group the Goodtimers. The song achieved greater success later that same year when it was recorded by Chubby Checker the following year, becoming his second US #1 (after his 1960 single ‘The Twist.’). It also topped the US R&B chart. ‘Pony Time’ does bear a resemblance to ‘The Twist‘, first recorded in 1959 by Hank Ballard & the Midnighters.”
Chubby Checker, “Pony Time” (1960):