Does a father have to pay BACK child support if another man has been on the birth certificate for the length of childs life?

It depends upon the state in which the minor child resides. The majority of U.S. states have a statute of limitations concerning the filing and awarding of child support monies. Aside from that issue, if the male who is named as the father by the biological mother does not voluntarily accept responsibility a paternity test will be required before child support matters are pursued. Whether or not the "father" can be ordered by the court to take such a test might also become a complicated legal issue.

FYI, generally the law presumes whomever is named on the original legal birth certificate is the father of the child. If said person made no objection to the designation at the time of the birth it is unlikely that a court would hear a motion to take action against another the now alledged father.