A medial ligament sprain is rare but can occur particularly with a fracture. This happens when the ankle rolls the other way, so the sole of the foot faces outwards, damaging the ligaments on the inside of the ankle.
The most common damage sustained in a sprained ankle is to the anterior talofibular ligament. This ligament, as the name suggests, connects the talus (ankle bone) with the fibula (smaller of the two bones in the lower leg). If the sprain is severe there might also be damage to the calcaneofibular ligament (connects the heel bone to the fibula) which is further back towards the heel. This ligament only becomes injured in more severe injuries due to its increased strength and laxity whilst the toes are pointed (a common position for ankle sprains).
In addition to the ligament damage there may also be damage to tendons, bone and other joint tissues, which is why it is important to get a professional to diagnose your ankle sprain.