If you are a parent who is also applying for PR, you can include your children in the PR application. A family application is always recommended way instead of a solo application.
If you are already holding PR status in Singapore, but your child is not ( e.g. A baby born recently), you can file an application only for the child under the scheme for “Children below 21 years old born to a PR”.
In case you are not a PR, but if you want to apply for PR for your child studying in Singapore in a local education scheme, you can apply for his / her PR under the student scheme.