Is there a way to trigger an immediate push replication for specific artifacts and not the whole folder in JFrog Artifactory?

I referred to the REST API documentation here. It works for folders. However, it is not working for individual artifacts.

There is not REST API method for triggering replication for a specific artifacts.
You can use the event-based push replication instead or on top of the scheduled replication - artifact replication will occur in nearly in real-time since each create, copy, move or delete of an artifact is immediately propagated to the far end.

If you wish to limit the artifacts being replicated to a given path you can:

1. Configure a "Path Prefix" - Only artifacts that located in path that matches the subpath within the remote repository will be replicated
2. Create a custom user plugin with a replication execution point - plugin can have logic to decide whether to replicate or skip based on the artifacts path