Adam Clarke on 1 John 2:12

I write unto you, little children - Τεκνια· Beloved children, (see on 1Jn 2:1 (note)), those who were probably the apostle's own converts, and members of the Church over which he presided. But it may be applied to young converts in general; those who can call God Abba, Father, by the Holy Spirit: therefore he says of them, that their sins were forgiven them for his name's sake: i.e. on account of Jesus, the Savior, who had died for them, and was now their Mediator at the right hand of God.