In the New Testament, the symbol of the Fish links between Christ with his followers; As he walked by the Sea of Galilee, he saw two brothers, Simon who is called Peter and Andrew his brother, casting a net into the sea; for they were fishermen. And he said to them, “Follow me, and I will make you fishers of men.”  
Matthew 4:18-20
The fish symbolize Christ, the newly baptized and the Eucharist. There are few sources to that symbol:
It is the Greek word for a fish - "ΙΧΘΥΣ" it also an acrostic of the verse "Ίησοῦς Χριστός, Θεοῦ Υἱός, Σωτήρ", Meaning: "Jesus Christ is the Son of God". The source to it is from acts 8 "And as they went on their way, they came unto a certain water: and the eunuch said, See, here is water; what doth hinder me to be baptized? And Philip said, If thou believest with all thine heart, thou mayest. And he answered and said, I believe that Jesus Christ is the Son of God."
Acts 8:36-37