How can my child's father see him if he is illegal?

The father of your child should consider applying for a visitor's visa that would allow him to enter the U.S. for a visit and then return home. This may be problematic if he is unable to persuade an immigration official of his genuine intention to enter the U.S. only temporarily, of if there may be some other legal impediment to lawfully getting a visa; there is no substitute for engaging an immigration attorney to carefully review all of the relevant details and to advise about eligibilities, options and strategies.