The Spirit himself bears witness with our spirit that we are children of God, (ESV)
Those whom the Lord has called unto himself are adopted as sons and daughters. Adoption was a big deal in the Roman culture. Dr. John MacArthur writes the following: "In Roman culture, for an adoption to be legally binding, seven reputable witnesses had to be present, attesting to its validity. (MacArthur Online Study Bible Notes)"
What is the witness that we have been adopted by God? Paul tells us that the Spirit himself bears witness with our spirit that we are children of God. Many people have taken this verse and insisted that we will experience some sort of mystical or emotional feeling if we are truly adopted. The problem is that is not verified anywhere in Scripture.
We do have passages in Scripture which help us to understand what happens to truly adopted children of God. In Galatians 5:22-23 Paul describes the "fruit of the Spirit." If the Holy Spirit is living in you, as a truly adopted child of God you should produce the fruit of that Spirit witness. The fruit is: love, joy, peace, patience, kindness, goodness, faithfulness, gentleness, and self-control.
In addition to the fruit of the Spirit we will find that an adopted child of God exhibits the power of the Spirit. Consider that the same spirit that raised Christ from the dead is living in you. That power is going to be expressed in your life. Acts 1:8 reminds us that the power we have to be witnesses for the Gospel comes from this very Spirit that bears witness with our spirit that we are children of God.
If you are adopted by God others will know it. They will see it by the fruit the Spirit is producing in your character. They will also see it in the powerful way you stand up for the Gospel. Is the Spirit bearing witness with your spirit that you belong to God? Can others see it?