With the User input service you need to use InputChanged (not InputBegan) to detect mouse wheel movement and with the Z position of the input you can determine if the mouse wheel is being moved up or down. So for example:
local UIS = game:GetService("UserInputService")
UIS.InputChanged:Connect(function(input)
if input.UserInputType == Enum.UserInputType.MouseWheel then
if input.Position.Z > 0 then
print("Mouse Wheel UP")
else
print("Mouse Wheel Down")
end
end
end)