From 1965 through 1968 Kim Braswell was the placekicker at Avondale (Georgia) High School. During that time he attempted 134 points-after-touchdown. He made good on all 134. He also tried three field goals, from the 43-yard line, the 38-yard line, and the 33-yard line. He made good on all three attempts.
From The Giant Book of More Strange But True Sports Stories by Howard Liss. Illustrations by Joe Mathieu.
The article is an interesting read. I couldn’t set it as a regular link because it kept embedding in the page and then doesn’t look like an embed on the “live” page. His record was broken in 2015, but the record doesn’t state who broke it. He’s also self-aware enough to recognize that his record was also the result of a lot of luck and the work of the other players he depended on.