If you want to run a specific version of Neo4j and install the software via a debian repository you need to use a technique called apt pinning. Otherwise, any system update will also update Neo4j to its latest stable version.

As an example assume you want to make sure to stay on 3.5.x versions - effectively preventing an upgrade to 4.x or higher. To use apt pinning create a file /etc/apt.d/preferences.d/neo4j with these contents: