Thanks for your question. Only one parent can claim "an amount for eligible dependent" for the dependent. If one parent has already claimed the dependent, then the other parent can't claim the same dependent in the same tax year. Please click here for more information.
Thank you for your question,
1. Eligible Dependant Tax Credit
As per CRA, generally, if you are required to make child support payments to a current or former spouse or common-law partner for a child, you cannot claim an amount for an eligible dependant on line 30400 for that child.
If you and another person each have a clearly established requirement under a court order or written agreement to make child support payments for a child, normally neither of you would be able to claim the amount for an eligible dependant for that child. However, in this case, you may still be eligible to claim the amount for an eligible dependant, as long as you and the other person agree that you will make the claim. If you cannot agree, neither of you can claim an amount for an eligible dependent for that child.
Please read the article Child custody and the amount for an eligible dependant to learn more about child custody and eligible dependant tax credit.
2. Canada Child Benefit
CRA offers Canada Child Benefit, which is a non-taxable benefit, for each eligible family to cover the cost of raising children under the age of 18. Children with disabilities will receive an additional amount for the Child Disability Benefit. The benefit is paid when you register the child after birth and will stop automatically when the child turns 18. For a single parent, the parent with custody is the one who receives the benefit. For shared custody, the benefit is either split in half or according to the custody agreement.
3. Canada Caregiver Tax credit
If you have a child who has infirmity or disability, you can claim the Canada Caregiver Amount for your child or your spouse/common-law child. You can claim this amount for as many children as you have. For a single parent with shared custody, only the parent who claims the Eligible Dependent Amount will be able to claim the Canada Caregiver Amount for the same child.
Please visit the Turbotax article on Family Tax Deductions: What Can I Claim? to learn more about tax deductions.