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Genrerally, courts will not even entertain a request for modification unless there has been a significant change in circumstances......which generally involves a move, a remarriage, an issue of child neglect, drug abuse/substance/alcohol abuse, etc. So, if none of that is present, it is very unlikely that the court would grant him joint custody.
Also, if he's not in the child's life and provides no financial support for the child, the probability of him getting anything other than some form of visitation would be very low.
If there is no order for child support in place, you should also consider asking the court to enter an order establishing that.