Make sure you do not have disagreements about your son, in front of him. Any discussions should be done much later, when he is out at school or asleep in bed. You do need to set some rules which you both can agree to - but it is early days - you say you have only lived together for four months. This is a huge adjustment for this little boy as much as anyone else.
Whether he is your biological son or not (which I think you are focused on) these problems could be happening anyway. Parents do have different styles of parenting, mum generally are closer to their young children than dads, kids do play their parents against each other anyway.
Relax and give it time, this is a huge adjustment for everyone, maybe your wife is feeling overprotective because she is aware of the impact it is having on your son.
As long as you do not have arguments about him, in front of him, and have discussions calmly out of his earshot, I think you could stand back and allow your wife to parent your son (lots of men do), so long as he is not disrespectful to you. In the long term you need to support each other with bringing up this little boy, but you need to agree with each other, and it will take time.