This comes in the form of post-secondary support for college. This page discusses which States permit post-secondary and post-majority support orders: Post-Majority Child Support Laws.
Family courts have been inconsistent as to whether or not to require custodial parents to bear some of the financial burden and contribute to the post-secondary support for college. In many cases they have ruled that the custodial parent did not have to share the costs, or was allowed to pay a reduced amount compared to the non-custodial parent.