It happens in the “Kebra Nagast,” the origin story of the Ethiopian royal family.
Beginning in the 13th century, Ethiopia was ruled by a royal family that practiced Oriental Orthodox Christianity and claimed to be descended from Solomon.
The oldest known edition of the “Kebra Nagast” (“The Glory of Kings”) is from around then, though we know it was translated from earlier versions in Arabic and Coptic and may have originated in the 6th century.
It says that during the Queen of Sheba’s visit with Solomon, she promised she would not take anything from his house without asking. He then proceeded to feed her very spicy foods and not give her any water.
In the middle of the night, she woke up desperately thirsty and poured herself a glass of water. Solomon basically said, “Gotcha, you promised you wouldn’t take anything. Now I get to ask you something.” He asked for a sexual relationship with her that resulted in the birth of a child, Menelik I.
According to the “Kebra Nagast,” when Menelik came of age, he decided he wanted to meet his father. Solomon offered to give Menelik I the throne because he was technically his firstborn, but Menelik didn’t want this. Instead, he said he would go home and have his people follow Solomon’s religion.
As he was leaving, someone in Menelik’s retinue grabbed the Ark of the Covenant and brought it back to Ethiopia. And so the story goes that they restarted the covenant between God and the Jews there and then eventually converted to Christianity.