Romans 8:16: “The Spirit himself testifies with our spirit that we are God’s children.”
One way to understand that you are a child of God is by reading the Bible. It is there. It is in the Bible. The Book testifies about the fact that you are born again and can righteously be called the son (or the daughter) of God. That is the most solid testimony that you can have about being part of the family of God.
The second very important testimony that is also very strong is the testimony of the Holy Spirit. If you are born again the Spirit of God lives in you and testifies to you about your nature. He calms you down and gives assurance that you are the child of God. Blessed be his holy name.