How would I make an area attack do damage to players over time?

If you already have a working script, you're going to want to create layers so that when the player moves through it they take damage, or a loop that damages any players within it for a certain amount of time. the loop, based on your question, should be wait(1).

I made a script to put in the part, it has issues with it and doesn't work much but here it is.

local Settings = {
    ['TimeWait'] = .2, -- How long per run
    ['Damage'] = 5, -- Damage per Run
}


local using = false

script.Parent.Touched:Connect(function(part) -- Part Touched
    if game:GetService("Players"):GetPlayerFromCharacter(part.Parent) then -- Checks if the part is a player
        if not using then
            if part.Name == "Left Leg" or part.Name == "LeftFoot" or part.Name == "HumanoidRootPart" then
                using = true
                print("Using")
                local humanoid = part.Parent:WaitForChild("Humanoid")
                while using do
                    humanoid.Health = humanoid.Health - tonumber(Settings.Damage)
                    wait(tonumber(Settings.Damage))
                end
            end
        end
    end
end)

script.Parent.TouchEnded:Connect(function(part)
    if game:GetService("Players"):GetPlayerFromCharacter(part.Parent) then -- Checks if the part is a player
        if part.Name == "Left Leg" or part.Name == "LeftFoot" or part.Name == "HumanoidRootPart" then
            if using then
                using = false
                print("Not Using")
            end 
        end
    end
end)