My ex previously said she claimed both children as eligible dependents. Is this possible, or could i have claimed one of the children?

[TurboTaxKim]

The CRA rules about claiming the Eligible Dependant Amount (EDA or  Equivalent to Spouse) only allow one claim per single, separated or divorced person. Your ex-spouse may have included both children on her tax return for the calculation of other credits and benefits, but could only claim for one child for the Eligible Dependant Amount.

In order for you to make a claim for one of the children as an Eligible Dependant, you must meet certain CRA requirements such as having shared custody and are not eligible to make the claim for one child simply because the other parent is not claiming that particular child.

If you are required to make Support Payments for that child, you are not able to make the claim for the Eligible Dependant Amount. However, if you and the other person both had to make support payments for the child for 2019, you claim this amount only if you and the other person(s) paying support agree you will be the one making the claim for that child. 

Please see the following links for more information: TurboTax - Claiming the Eligible Dependant Amount and What are the situations in which you cannot claim the amount for an eligible dependant?