"When a player joins the game, the provided code creates a part in the workspace. The part is then added to the Hitboxes folder and its properties are adjusted. Additionally, the part is cloned for each new player and exclusively assigned to them."

```lua
-- server script (ServerScriptService) 
game.Players.PlayerAdded:Connect(function(player)
    local part = Instance.new("Part", game.Workspace)
    part.Name = "PlayerPart"
    part.Size = Vector3.new(4, 1, 4)
    part.Position = Vector3.new(0, 50, 0)
    part.Anchored = true
    
    -- Adjust properties as needed 
    part.Color = Color3.new(1, 0, 0) -- Example: Changing color to red
    
    -- Create or ensure Hitboxes folder exists 
    local hitboxesFolder = game.Workspace:FindFirstChild("Hitboxes")
    if not hitboxesFolder then
        hitboxesFolder = Instance.new("Folder", game.Workspace)
        hitboxesFolder.Name = "Hitboxes"
    end
    
    -- Move part to Hitboxes folder 
    part.Parent = hitboxesFolder
    
    -- Clone part for the player 
    local playerPart = part:Clone()
    playerPart.Parent = game.Workspace
    playerPart.Name = player.Name .. "'s Part" -- Naming the part after the player
    -- Adjust additional properties or add scripts to playerPart if needed
end)
```