1. Mathew 2 has Joseph take his family to Egypt and then return while Jesus was "young child". Luke 1:80 has Jesus in the desert which Egypt is not.
2. Barjesus is similar to the modern name Johnson. Why you assume this Barjesus is the son of a biblical Jesus rather than one of the other thousands that borne that name is confusing. It is made more illogical since this reference occurs in Acts which took place (supposedly very recently after the cruxification within 10-15 years). Since Jesus does not meet Mary until he start his teachings at 30 dieing three years later any son of his would be extremely young, no older than 15.
3. Jesus Justus was not the son of Marc Antony and Cleopatra. They had 3 children both sons Alexander Helios and Ptomley Philadelphus died young (though Ptomley may have survived). Also Marc and Cleo died in 30BC which is 30 years prior to the birth you contend this Jesus had.
In mainstream Christian belief both Barjesus and Jesus Justus are consider separate from Jesus Christ. The Christ was born to Mary around 1AD, preached in Jerusalem, was killed by Pilate, and then rose to take his place in heaven. He is to return to judge the living and the dead and his sacrifice is meant to be the salvation of mankind.
Now I believe all that to be nonsense but the OP take this nonsense and tries to adds several layers of more nonsense to it.
