Is it possible for a spirit to eat fish? Then how did Jesus eat fish after his resurrection (Luke 24:43).
Most branches of Christianity believe that Jesus rose from the dead bodily (ie he wasn't merely a spirit at that point). The very context of the verse you are referring to, is that he was eating the fish to show he was not a ghost to his disciples:
Jesus Appears to the Disciples
36 While they were still talking about this, Jesus himself stood among them and said to them, “Peace be with you.”
37 They were startled and frightened, thinking they saw a ghost. 38 He said to them, “Why are you troubled, and why do doubts rise in your minds? 39 Look at my hands and my feet. It is I myself! Touch me and see; a ghost does not have flesh and bones, as you see I have.”
40 When he had said this, he showed them his hands and feet. 41 And while they still did not believe it because of joy and amazement, he asked them, “Do you have anything here to eat?” 42 They gave him a piece of broiled fish, 43 and he took it and ate it in their presence. - Luke 24:37-43 NIV, emphasis added
A related question along these lines is found here: How similar was the resurrected body of Jesus to his physical human body?