Can citizen parent adjust status of unmarried 23 y/o Overstayed son?

As a U.S. citizen, you can petition for your son (assuming you and your son meet all eligbility requirements). However, there are significant wait times for visa availability for adult sons/daughters (length of the wait depends on what country he is from). If he had an approved petition and a visa number available (again, this would take time), he could possibly consular process with a waiver (based on hardship to his US citizen parent).  I say possibly because he would have to make sure he is not subject to any other bars that would prevent visa issuance and he would have to be able to prove hardship to you. Your son is most likely barred from adjusting his status because he has been accruing unlawful presence since he turned 18 (unless something has been tolling his unlawful presence). I'd also look into the possibility of 245i grandfathering. Your son's situation is complicated and it would be worth consulting with an experienced immigration attorney to see what, if any, options may be available to him.