Does a new born baby carry the dna of all the men the mother had sex with prior to its conception?

No, because in a Punnett Square it only uses two patents DNA

Definitely, the answer for this question would be no. It is not true that a newborn baby carries the DNA of all the men the mother had sex with prior to its conception. The only DNA that the newborn carries is from the its mother and father only from where the sperm and the egg cell is, that formed the newborn baby. The formation of the DNA only happens once the egg cell of the mother and the sperm cell of the father unites. Hope this helps.