How do you limit the first person cameras range of motion?

Alright, a few changes hope this helps:

local camera = workspace.CurrentCamera
local player = game.Players.LocalPlayer
local character = player.Character
local humanoid = character.Humanoid

player.CameraMaxZoomDistance = 0.5
camera.FieldOfView = 110
humanoid.CameraOffset = Vector3.new(0, -1, -1)

for childIndex, child in pairs(character:GetChildren()) do
	if child:IsA("BasePart") and child.Name ~= "Head" then

		child:GetPropertyChangedSignal("LocalTransparencyModifier"):Connect(function()
			child.LocalTransparencyModifier = child.Transparency
		end)

		child.LocalTransparencyModifier = child.Transparency

	end
end