Object-level replication of cloned objects from a source file system to a target file system in a data storage system maintains relationships between related objects including shared data blocks so that storage requirements in the target file system match storage requirements of the source file system. Specialized processing may be used to scan an indirection object that refers to other file system objects such that objects requiring replication can be identified on an incremental basis based on checkpoint numbers. Checkpoints in the target file system are managed so that checkpoint number requirements for replicated clone objects are enforced in the target file system.