There are three views on this:
Timothy was with Paul when this letter was written and Timothy was the one who wrote the letter while Paul did the authorizing. However, the personal reference throughout the letter does not support this theory of joint authorship.
Timothy may have been well known to the Gentiles churches there, so by associating himself as brother with Timothy, Paul may also have in mind that this brotherhood will connect him with the brotherhood of the Colossian believers. This theory implies that Paul may need Timothy’s acknowledgement to address the believers in Colossae. This theory does not go along with what Paul said about himself already.1
Timothy was with Paul when this letter was written. Colossians 2:1 gives the possibility that there may be some believers among the Colossians who may have met Paul face to face, perhaps as a result of his ministry. Therefore, knowing that Timothy was involved with Paul in his ministry, these believers were known to Timothy also.2
1 Paul, an apostle of Christ Jesus by the will of God, and Timothy our brother,