The royal lineage of Jehoiakim continues directly through his son and grandson. His son Jeconiah, also known as King Jehoiachin, was taken captive to Babylon, where he remained for many years until the end of his life [ביאור שטיינזלץ].
Jeconiah's line then continues with his son, Zedekiah. While the name is familiar, it is important to separate this individual from the famous King Zedekiah. The well-known king was actually Jeconiah's uncle, the son of Josiah. The Zedekiah present in this generation is instead Jeconiah's biological son [מצודת דוד]. The shared name is simply the result of a family tribute, as Jeconiah chose to name his own son after his uncle [רד״ק].