An event that occurs halfway through is referred to a midterm event. Like a midterm exam. What if it occurs at 1/3 of the time, or at 2/3.
"A third of the way through, " or
"At the one third point"(little awkward),
"Around the one third mark", (slightly informal)
Halfway is common enough to be used directly. Other fractions can follow:
"A quarter of the way though"
"A fifth of the way,"
"At the 15% mark,"
For exams, Midterm is a special name. There are no "tri-term" exams and such. Just Midterms and Finals. Outside of tests, elections, or perhaps pregnancy, I've not heard Midterm used.