A simple "hey SS, how about some quiet time please? If you can't do that, go play in your room" should be fine. We do this with SD6. We're always gentle and kind about it, but sometimes kids need to know they're annoying you or invading your mental capacity at the moment. Sometimes when we ask for quiet time, she'll keep rambling - trying to bring us into her games/play or keep conversations going and we'll remind her that if she doesn't give us some quiet time, she'll be sent to do XYZ in her room.

"SS your dad and I are having a conversation at the moment and it is rude to interrupt, please wait your turn."

This is possessiveness and his father needs to set a limit on it - "June Ann just got home from work and I'd like to spend some time with her. Go ride your bike."

It's normal for a kid to be worried about his place in a new family, but Dad needs to make clear that the adults are in charge.

DUP

This child is insecure.  Dad needs to let him know he is loved and not being replaced and then let him know such continued behavior is not ok.  I like the idea of "go find something to do and give us a few minutes" and then "If you don't, you will be finding something quiet to do in your bedroom.

Address it directly, "It is rude to interupt otehrs conversations." If his doesn't work or Dad allows Skid to interupt - walk away. Go do something for yourself - read, bath, etc. 

Definitely begin to shut that down immediately.  It's annoying as hell and it will just get worse.  

You Fiance needs to deal with this.

When my Fiance and I first started dating his son always wanted to be in the middle of us. It was not a possessive thing, it was he love being the center of attention, also loved the idea of he might have a mom and dad.

Part of it is typical behavior at this age. My SS will do things when new people are around to get attention and all the focus on him. Drives me nuts but lots of kids this age do it. (My SS will be 10 soon). He also use to try to get in the middle of us while we hugged to hug both of us. My SO started pushing him out of the way and said hey I want to give her a hug alone. With the sitting in the middle he would say I want to sit with her next to me.

SS was still there and very present and trust me this kid knows he is loved and wanted but he also knows we are the adults and the parents and what we say is what happens in our home. Kids adapt and they take their cues on how to behave from the adults around them. If you finance continues not to correct this behavior you SS might start thinking he rules the home not his dad or you.

You need to do what is right and go with your gut on how to deal with this talk to him and if you know your fiance is good with you correcting his son, by all means do it.