Titus is mentioned as a companion of Paul in some of his epistles (2 Co 2:13; 7:6,13,14; 8:6,16,23; 12:18; Gal 2:1-3; 2 Tim 4:10).
Timothy is mentioned in Acts 16-20, and appears in 9 epistles either as joining in Paul's greetings or as a messenger.
In addition, Timothy has two New Testament letters addressed to him, and Titus one. From these three letters (called the Pastoral Epistles), it appears that Paul had comissioned Timothy to oversee the Christian community in Ephesus and vicinity, and Titus to oversee that in Crete.
The Pauline authorship of these three letters has been disputed by many scholars who accept as genuine most or all of the other New Testament letters attributed to Paul. In this connection, we may note:
It would be difficult to forge a letter from Paul to an early Christian community. If you did it during Paul's lifetime, the congregation would be likely to reply, thanking Paul for his letter, and he would write back, saying, "What letter?" If you forged a letter from Paul to (say) the Corinthians after his death, sooner or later the Corinthians would hear of the letter, and say, "If Paul wrote that letter to us in his lifetime, why has no one here ever heard of it?" These difficulties are less when one forges, say, a letter from Paul to Timothy, waiting until after the death of both to do so.
There are significant differences in manner between the Pastorals and the other letters. In his letters to churches, Paul routinely presents arguments for the positions he takes. In the Pastorals, he simply states his position and expects that to end the matter. However, it is a matter of common observation that a man may have one style when lecturing to a classroom and another when explaining something to a member of his family. (Hence the saying: Never teach a family member--or let a family member teach you--how to drive a car. The lesson is bound to lead to a shouting match.)
The subjects Paul deals with in the Pastorals are different from those in the other letters, and imply a much more formal church organization. However, it may be noted that Paul normally writes letters dealing with the questions that the recipient has asked, or needs to have answered. He writes to the Thessalonians about the Second Coming because some of them have gotten the idea that it is just around the corner, and so there is no reason to plant the crops. He writes to the Corinthians about the Lord's Supper, because of reports that some of them are behaving irreverently at celebrations thereof. (If the Corinthians had observed proper decorum at the Lord's Table, there would now be scholars who argued that Paul had never heard of the Eucharist, since he never mentions it.) It is not surprising that, having set Timothy and Titus to organize the church in certain areas, he writes to them about church organization.
The preceding remarks are not intended to settle the question of Pauline authorship, or even to present all the arguments on either side. They are merely there to get the reader started.