It gets a bit confusing for our clients as the guidance for minor child passport holders in Canada differs to that of the United States.
For holders of a US passport under the age of 16
Opposite to the guidance for Canadian passport holders. Your child should sign their own if they are able, but if they are too young to do so themselves a parent or legal guardian may print the child's name and sign themselves, then must also note their relationship to the child.
Quoted from the US Department of State website:
"What do I do if my child is too young to sign his or her passport book? A parent or legal guardian may sign the passport if the child is too young to sign his or her own name. To do so, a parent or legal guardian must print the child’s name and sign his or her own name in the space provided for the signature. The parent or legal guardian must also write his or her relationship to the child in parenthesis next to the signature (e.g., parent or legal guardian) so we know who signed for the child."
See the original resource at travel.state.gov here > LINK HERE
For Canadian passport holders under the age of 16
Basically, if your child cannot sign themselves, do not sign it on their behalf.
Quoted from the Government of Canada website:
"All children should carry a valid Canadian passport when they are travelling or living abroad. Children under the age of 16 can sign their own passports. If they do not, leave the signature block on page 3 blank. If you sign it on behalf of the child, the passport will be invalid."
See the original resource at travel.gc.ca here > LINK HERE
If in doubt, contact your local passport office or refer to the official resources linked above.