Nothing is known of this child, born of Pureblood parents Charlus and Dorea Potter sometime between 1940 and 1977 (based on Dorea being born in 1920 and dying in 1977). As part of the Potter family, this son would be a direct relative of Harry Potter. However, he presumably died before Harry was born, since Harry had no living relatives.
This son of Dorea and Charlus appears on the Black Family Tree with no name provided.
His maternal grandparents were Cygnus Black and Violetta Bulstrode Black. His aunts on his mother's side were Cassiopeia Black and Irma Crabbe Black, who married his uncle Pollux Black. He also had an uncle on his mother's side named Marius who was a Squib.
Ever since the Black Family Tree was made public, fans assumed that the son of Charlus Potter shown was James, and that Dorea and Charlus were his parents. This didn't exactly fit the comments Rowling had made that James' parents had been elderly when they had him and that they had died at a very advanced age, but the cryptic "Son" listed on the Tree seemed like a massive hint. This might indeed have been Rowling's intention when creating the Tree, but when she took the time to create the actual history of the Potter family, she created brand new characters as James' parents with a very interesting back story. This relegated the "Son" on the Tree to being nothing more than a small mystery, perhaps never to be solved.