Part 1 - We have communion with God, but our communion is specific - we have a distinct fellowship with each Person of the Trinity.
Christians are assured by John that the fellowship of believers (the invisible church) is "and indeed (or truly) our fellowship is with the Father and with his Son Jesus Christ." (1)
John uses the "indeed" or "truly" to give us the force of his declaration. He doesn't just want us to know this, he wants us to absorb this.
The next paragraph I'm going to do backward:
The world will ask: Why should I want communion with "them" (believers). Communion with them will bring nothing but trouble, shame, mocking and all sorts of bad things.
But believers do invite the world to join them in fellowship, they invite unbelievers to partake with them the precious things of eternity.
To the world, these believers looked like the were the dregs of society, "very mean and contemptible". Their leaders were counted as filth and rubbish. Why would the world want fellowship with them?
The Text of the book: Part 1. Of Communion with each Person distinctly - of Communion with the Father
Chapter 1.That the saints have communion with God — 1 John i. 3 considered to that purpose — Somewhat of the nature of communion in general.
IN the First Epistle of John, chap. 1, verse 3, the apostle assures them to whom he wrote that the fellowship of believers “is with the Father, and with his Son Jesus Christ:” and this he does with such an unusual kind of expression as bears the force of an asseveration; whence we have rendered it, “Truly our fellowship is with the Father, and with his Son Jesus Christ.”
The outward appearance and condition of the saints in those days being very mean and contemptible, — their leaders being accounted as the filth of this world, and as the offscouring of all things, — the inviting others unto fellowship with them, and a participation of the precious things which they did enjoy, seems to be exposed to many contrary reasonings and objections:“What benefit is there in communion with them? Is it any thing else but to be sharers in troubles,reproaches, scorns, and all manner of evils?”
(1) 1 John 1:3
Communion With God, by John Owen, Christian Classics Ethereal Library