Jesus Christ and the Sons of Cleopatra

The identity of Jesus Christ is an area I am researching extensively.  Where is the written record of him, other than the bible?  Before we can answer this question, let's take a look at something that was occurring near the "time" of his life.  It was the power struggle between Rome and Egypt.  Cleopatra VII and Caesarion were the last Pharaohs of Egypt.   Julius Caesar was the father of Caesarion.   Here is what they all looked like according to ancient art:

Bust of Cleopatra VII, Altes Museum, Berlin