What ligaments are involved in a high ankle sprain?
A high ankle sprain goes by more than one name, and the ligaments involved have a name of their own.
The short answer: the high ankle ligaments
Cleveland Clinic says "A high ankle sprain is also called a syndesmotic injury." It then explains that "This name refers to the syndesmosis, or high ankle ligaments." In plain words, the ligaments involved are the syndesmosis, the group of high ankle ligaments.

Why the name matters
If a clinic note says "syndesmotic injury," it is describing the same thing as a high ankle sprain. Knowing both names helps you follow your paperwork and search for the right information. This page stays with the names the source gives and does not guess at more detail.
Reading further and what to do next
To go deeper, the Cleveland Clinic page on high ankle sprains is the best place to start. The Cleveland Clinic page on sprained ankles covers ankle sprains more broadly. If your ankle will not bear weight comfortably or the pain keeps going, book a visit with a clinician near Woodland Park and ask which ligaments were affected.
The short version
The name tells you which part of the ankle to ask about. Which ligaments are actually injured in your case is a question for an exam, so bring that question with you.