Structuring backend queries

So this is more of a methodology question than a coding question. I want to ask this before I actually start coding in order to choose the best route. I have a messaging app. When the app launches I query in the background all the messages from the backend where current_user_id is equal to recipient_id. Now I have all of the messages stored the user needs to see so I locally store them into a sqlite database.

Great, but what about when the user gets new messages? How can i structure a query to receive those without having to query the entire table again? Also how do I set this up as a continual process? Is the phone always requesting update information from the backend while its in the foreground?

Thanks. I really appreciate your help. I'm currently using iOS and as stated SQLite. Also my backend is AWS node.js.