1990s Superboy was given the Kryptonian name "Kon" and also invited in to the "El" family, and that he's a clone of Clark and what's his name from Cadamus, which Cereal Lord retconned to his fanfic of Luthor.
Jonathan Samuel Kent (the current Superboy) is the genetic and biological child of Lois and Clark from Convergence and Arrival, etc.
Clark Kent, Jr. (if you mean Superman Junior) isn't really presented as Lois and Clark's kid, even if that computer simulation Clark and Bruce were running. And if you mean something else, well there are a ton of imaginary and dream and otherwise stories of Lois and Clark having multiple male and male/female and all sorts of Super Babies.
The NEW 52 Superboy needs to be treated as an alternate future possible Superboy since that character was never "KON-EL."
He was just "Kon" and even then it was pretty rare, I think it was only used once in Teen Titans until Lobdell shat the bed even more in Krypton Returns when Harras got him assigned back on the Superman book, and then claimed that "Kon" was Kryptonian for Clone, and made that army of Kryptonian Clones who all coindic looked like teen Clark. THAT "Kon" also never went by Conner, I'm 99& certain and definitely isn't a Cadamus doctor/baby daddy or Lex/baby daddy part clone, he supposedly is part Lois/Clark and some future chrono infused villain.
With all the Superman Reborn stuff, Conner should still be around/alive.