Why is Gilgamesh considered to be one-third human and two-third god? Most of the time, the term "demigod" is used to describe people who are the offspring of a god and a human. As far as I know, Gilgamesh is the child of a goddess and a king. Why then is Gilgamesh considered to be one-third human and two-third god when he is the offspring of a god(dess) and a human? Is there a story behind this, one that's about his conception?

Gilgamesh was a recurring character in Mesopotamian myths/stories. The most renown of those stories is the Epic of Gilgamesh where those numbers appears. But he and his slave/servant/friend/buddy/lover Enkidu are in numerous other stories. And in none other those funny proportions are mentioned.

It is also good to be aware that the Epic comes to us in various versions. There is no (right now) any complete version of the myth per se. It is just a reconstruction from different tablets.

Now the Epic does not give any rational explanation about the proportion. Just remind it is barely a detail trying to make clear Gilgamesh is far beyond any normal human being. As long as it is striking you enough as being "totally abnormal" the one who wrote it did succeed.