The sample below illustrates how you can read child projects of a project record by the child project type (project's 4-character unique code).
// in this sample, it is assumed there is an existing parent project record with a unique key String, parentKey
// it is also assumed that there are one or more child project records (where the custom object definition's unique code is "CLAI")
protected ProjectRepository projectRepository;
public void readChildProjectsForEntityType() throws Exception {
// in the list of child Projects returned, only the name properties will be returned
List<Project> children = projectRepository.readChildProjectsForEntityType(parentKey, "CLAI", Arrays.asList("name"));
}