In the verses following Matthew 5:17 and 18, Jesus explains what he means by fulfil. Jesus perfects the moral commands of the Law and the Prophets, making them even more strict: the command against murder is perfected in the command against anger; the command against adultery is perfected in the command against indulging in lustful thoughts, etc.
Galatians should be sufficient. However, if you would like additional passages, the following might also be helpful.
Matthew 19:16-19 where Jesus tells us which commandments of the Old Law must be kept in order to enter life. They are the moral laws of the Old Testament; none of the commandments regarding the sabbath, circumcision, dietary regulations, animal sacrifices, etc. is mentioned,
Mark 7:14-22 where Jesus tells us that only things that come out of the heart of a man can defile him; nothing a man touches or eats can defile him.
Acts 15 where the Apostles and presbyters met in council in Jerusalem and decided Gentile converts at the time should not be forced to keep most of the Mosaic Law.
Colossians 2, where Paul speaks against Judaizers, especially Colossians 2:16-17:
16Therefore let no one pass judgment on you in questions of food and drink or with regard to a festival or a new moon or a sabbath. 17These are only a shadow of what is to come; but the substance belongs to Christ.