My returns keep getting rejected because of an error message that says, "Rejection SEIC- F1040-506-02: On Schedule EIC" But the other parent did not claim the child

The rejection code indicates that your child was claim on another return. It does not specifically say it was the other parent's return. It means someone claimed the child on a return. 

 

If you know that the other parent did not claim your child, you have two alternatives.

1. Mail in your return to the IRS. Your refund will possibly be delayed when the IRS determines who is allowed to claim your child. You might receive letters from the IRS asking you to prove that you can claim your child on your return. With this alternative your entire refund could be delayed in the process.
2. Remove the child from your return and file electronically without the child. When you receive the refund on this return you should then submit an amended return adding the child back on the return. With this option only the incremental portion of your refund will be delayed during the process.

If you when you remove your child, you now owe taxes to the IRS you should select first alternative.

 

If you select the second alternative you will need to follow the steps on How do I amend my 2019 TurboTax Online return?