Assuming that the parties are unmarried the situation is pretty straightforward. There is no legal tie between the child and the male. The man registered as the father on the birth certificate is presumed to be the father, but this is rebuttable and as such proving that the child is not theres will sever the tie- blood testing/DNA testing can prove this conclusively, although circumstantial evidence such as impossible gestation period or unlikely conception can be used.
Hope this helps.