In you first sentence, serving time is a common expression.
He's serving time in prison.
He's serving time at the state penitentiary.
The second and third are less common because the phrase serving time is generally not broken up by another word when talking about somebody's current state. (It can be broken up and understood, but it doesn't happen as often.)
When the phrase serving time is broken up, it's normally done when referring to the past or future, rather than the present:
You've done your crime, now you'll have to serve your time.
She committed crimes and served her time for them.
So, while there is little difference between your sentences grammatically, your first is the most idiomatic when it comes to the present—because we commonly don't break up the phrase serving time.