Your dependent filed a return without saying he could be claimed on your return and your return was rejected?  AFTER his return has been fully processed and he has received his refund, he has to file an amended return that says he can be claimed as a dependent on someone else’s return.  Amended returns (form 1040X) have to be printed and mailed.  They cannot be e-filed; it takes the IRS a couple of months to process them.  Meanwhile, since your e-filed return has been rejected, you now have to print and mail it in to the IRS.  You will not be able to e-file.  Remember that when you mail a return, you need to include copies of your W-2, etc. with your return.

For your dependent:

https://ttlc.intuit.com/questions/2952222-how-do-i-amend-the-2016-taxes-i-filed-with-turbotax-online

So, if my son does his form and it takes a couple of months for a recognition, will that affect my tax return if I still mail them personally and I claim him as a dependent.

Mailed returns are processed differently so claim your son and mail your return. Your son's amended return could take several months to be processed. You do not have to wait for that;  go ahead and mail yours.

my refund wasnt rejected i just want to add my son ,i didnt know i could claim him because he lives with me