Bible has many fascinating questions and riddles. And only those who read it carefully and with full attention to the details can answer such tricky questions. They do not have any spiritual significance or meaning. It does not really matter who owned that bird, but the question is interesting.
The answer is Caiapha (or supposedly he is the owner), because the events described in Mark 14 took place in his house. He was the first priest at that time. Unless someone carried the rooster into his house on purpose or it belonged to one of his servants, he must have owned it.
This is an interesting question. Although it is not a very important one. You may find out more about Types of prayer: 10 top list for Nigerian Christians which is an essential part of Christian life here
The Scriptures do not clearly indicate who the rooster belonged to. However, we know that after being arrested in Gethsemane Jesus was first taken to the court of the Annas High Priest. Peter was not present there.
Later on Jesus was relocated to the Caiaphas’s court, who also was a High Priest that year. Peter followed Him there and that is where the denial took place. So, we can assume that the cock belonged to Caiapha or one of his servants, as it was kept in his yard. This is the best assumption we can make on this matter.
You can find the account of Peter disowning Jesus in the Gospel of Mark 14:66-72 and in Matthew 26:69-75.