update system service is a system app which has to do with updates. so the thing is that spyware can't be a system app. in order for that to happen, the spyware would need would need permission to read and write onto your system partition.......in other words your phone would need to be rooted. and rooting is not as easy as it used to be. rooting these days requires adb programming setup on a computer and your phone hooked up to it. so unless you handed a phone to someone who then attached to a computer, i doubt your phone is rooted.
i agree with
@puppykickr , what makes you think you have spyware on your phone?