You cannot schedule a specific project or task for the user to work on, but you can specify an activity, and require that work be performed against that activity. The adherence requirement will only apply to schedule users with Check Schedule Adherence permission.
Web TimeSheet administrators select which activities can be scheduled for each user while setting up templates or creating schedules for a user. The user (Web Timesheet administrator or Schedule Manager) must have a Web Schedule license seat assigned in order to make these changes.