how to add a hat to a character while following the rules of local script, and server script?

So a LocalScript can only be used locally for a player. In that case, you can use game.Players.LocalPlayer. Any changes made from a LocalScript will only be seen from the client, not anyone else in the server. If you'd like to clone a hat when a player first joins the game, then you would have to use PlayerAdded event.

This script will run everytime a new player joins. If you want the hat to clone everytime the player respawns, you should create a ServerScript and place it in StarterPlayer > StarterCharacterScripts. Since this script is in StarterCharacterScripts, it will be cloned into the player everytime the player respawns or joined. In this case, you're allowed to use both LocalScripts and ServerScripts. LocalScript changed are still made local because they are scripts only being run for the client.