How to export oracle 11g database partially
You can add a where clause to each table to filter rows exported:

http://www.dba-oracle.com/t_export_where_clause_selective.htm

However your referential integrity will not be maintained by this method, because the export is done per-object and filters are applied in the same way. You will need to either be very precise in how you define each where clause, which will make the export slow, or clean up the data afterwards by deleting any orphaned rows.

I would recommend creating a new schema in the same database and copying a chunk of the data into that, while maintaining the integrity during the copy. Then export the new schema.