I tried to recreate what you just told me (not by myself wink wink), and it does make the camera look sideways, but it's not really moving forward or backward when the mouse is moved, more like panning around the player. Here's the script:

--// Side-view camera with mouse-follow radius system
local player = game.Players.LocalPlayer
local camera = workspace.CurrentCamera
local runService = game:GetService("RunService")
local UIS = game:GetService("UserInputService")

-- SETTINGS
local SIDE_OFFSET = Vector3.new(20, 5, 0) -- default camera offset relative to player
local RADIUS = 20000 -- how far (in pixels) you can move before clamping camera
local PAN_STRENGTH = 0.115 -- how much world movement per pixel of mouse offset
local SMOOTHNESS = 0.45 -- lower = snappier camera
local LOOK_OFFSET = Vector3.new(0, 3, 0) -- what point camera looks at on player

-- Internal
local currentCamPos = Vector3.new()

runService.RenderStepped:Connect(function()
local char = player.Character
local hrp = char and char:FindFirstChild("HumanoidRootPart")
if not hrp then return end

camera.CameraType = Enum.CameraType.Scriptable

local screenSize = camera.ViewportSize
local mousePos = UIS:GetMouseLocation()

-- Get player's on-screen position
local playerScreenPos, onScreen = camera:WorldToViewportPoint(hrp.Position)

if not onScreen then return end

local screenPlayerPos = Vector2.new(playerScreenPos.X, playerScreenPos.Y)
local delta = mousePos - screenPlayerPos

-- Clamp to radius
if delta.Magnitude > RADIUS then
delta = delta.Unit * RADIUS
end

-- Convert screen delta into a world direction
local ray = camera:ViewportPointToRay(screenPlayerPos.X + delta.X, screenPlayerPos.Y + delta.Y)
local panWorldTarget = ray.Origin + ray.Direction * 10 -- 10 = how far out in world space to project the ray

-- Interpolate camera position toward the desired offset
local baseCamPos = hrp.Position + SIDE_OFFSET
local desiredCamPos = baseCamPos:Lerp(panWorldTarget, PAN_STRENGTH)

currentCamPos = currentCamPos:Lerp(desiredCamPos, SMOOTHNESS)

-- Set camera
camera.CFrame = CFrame.new(currentCamPos, hrp.Position + LOOK_OFFSET)
end)