If you both live with the child, his father should remove the child from his tax return completely.
Since you have the higher AGI and pay more than half of the support of the home,
everything is on your return.
Your partner's return needs to be amended to remove the Earned Income Credit. He received this credit because he indicated that the child lived with him more than half the year. That wasn't technically "lying" on his part, but it led to a tax benefit that he shouldn't get.
Because he already efiled, you will not be able to file your return electronically. You will need to mail your return, as it will continue to reject. He should mail his amendment ASAP, so the processing of your return is not held up any longer than it needs to be.
On your return, you should indicate Head of Household and claim the child as a dependent. Your partner needs to amend and remove any vestige of the child from his return. When parents live together, its "winner takes all." The winner is the one with the higher AGI. Only parents who live apart can split up certain child-related benefits.
Please see this post- same issue:
https://ttlc.intuit.com/questions/3614064-how-can-i-claim-my-son-as-a-dependent-and-his-mom-claim-hi...
