My grandson filed his taxes for the 1st time, but claimed himself, when he actually lives with me, his grandmother. How do we fix this?

Does your grandson meet the requirements for you to claim him as a dependent?
How old is he?
Is he a full-time student?
How long did he live with you in 2017?
How much was his 2017 income?
Does anyone besides you provide any of his support?

MY DEPENDENT CLAIMED HIS OWN EXEMPTION

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. You do not have to wait for your dependent’s amended return to be processed.  Remember that when you mail a return, you need to include copies of your W-2, etc. with your return.

For your dependent:

Amend 2017

https://ttlc.intuit.com/questions/1894381-how-to-amend-change-or-correct-a-return-you-already-filed?jump_to=answer_3288565

And use a mailing service that will track your mailed return--like UPS or certified mail--so you will know they received it.

The 1040X will take about 16 weeks to process. Remember to also amend State if applicable.