The father needs to file for a modification of the custody order. The court would then take his concerns into effect to look at modification of the custody order. A six year old in likely not going to have much effect on the decision.
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It sounds like you may not yet have a custody order yet. If so, you would need to start with an original paternity action to get custody squared away to determine what is the best interests of the child. 6 years is probably too young for the child to have a say in where he wants to live. However, if there is a therapist or other expert who has worked with the child, that person may be able to help give an opinion of what might be in the child's best interest.
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