In Arc Catalog add a new field to the local instance of FISH.
Here's why we created an empty version of TEST on the remote SDE instance and ONLY replicate the TEST table. In the SDE "stack" there are lots and lots and lots of tables, functions, and stored procedures that handle things. Had we attempted to replicate TEST from the Publisher to the Subscriber without first having created the TEST feature class on the subscriber, none of the SDE dependencies would have been created and we wouldn't be able to use the remote TEST feature class in any GIS applications.
In this manner we can have a fully synchronized copy of TEST on both SDE instance yet the SDE "stack" on either instance independently manages the feature class without any interference caused by replication.
This is a personal blog and does not recommend, endorse, or support the methods described above. Alteration of data using SQL outside of the ESRI software stack, of course, is not supported and should not be applied to a production database without a thorough understanding and disaster recovery plan.