The name appears in multiple forms in historical sources, such as Gonoma, Guonimi, Gjonëmi, Ghionoma, Giolma, Gionima, Gonome, Jonema, Jonoma etc.

The first member of the family itself was mentioned in sources dating to the early 13th century as a vassal of Dhimitër Progoni in the Principality of Arbër.

Another member of the family, Vladislav Jonima, is mentioned in sources in 1306, with the title of župan, while in service of Stephen Uroš II Milutin of Serbia.

[9] In 1402, as part of the Albanian nobility that served as Ottoman vassals, Dhimitër Jonima fought alongside Bayezid I's forces at the Battle of Ankara.

At the beginning of the 15th century Shufada (an important former marketplace on the Adriatic sea, near Lezhë) was a possession of the Jonima family before in 1428 it came under the control of Gjon Kastrioti.