Matthew was a Jew who worked for the occupying Roman forces, collecting taxes from other Jews. Though the Romans probably did not allow extremes of extortion, their main concern was their own purses. They were not scrupulous about what the "tax-farmers" got for themselves. Hence the latter, known as "publicans," were generally hated as traitors by their fellow Jews. The Pharisees lumped them with "sinners." So it was shocking to them to hear Jesus call such a man to be one of his intimate followers.
Matthew got Jesus in further trouble by having a sort of going-away party at his house. The Gospel tells us that "many" tax collectors and "those known as sinners" came to the dinner. The Pharisees were still more badly shocked. What business did the supposedly great teacher have associating with such immoral people? Jesus' answer was, "Those who are well do not need a physician, but the sick do. Go and learn the meaning of the words, 'I desire mercy, not sacrifice.' I did not come to call the righteous but sinners" (Matthew 9:12b-13). Jesus is not setting aside ritual and worship; he is saying that loving others is even more important.
No other particular incidents about Matthew are found in the New Testament.