Can I directly query from prodigy database?

I store my training set in Neo4j database. Can I directly query from prodigy database and let them two databases interact?

Yes, that's no problem, you can interact with Prodigy's database from Python, add custom logic to your recipe to save annotations straight to your Neo4j database (e.g. using a recipe's update) callback, or write a custom stream to load raw data from your other database.

Here are some resources, depending on what exactly you want to do: