In most cases you can test paternity with 99.99% accuracy when the father is biologically related to the child. Also, you can 100% exclude a man as the father of a child unless that man has an identical twin who is the father. This can become very convoluted, but I will try to explain it below.
A quaternary marriage or relationship is when a pair of identical twins who marry or start a relationship with another set of identical twins. Quaternary marriage is a very rare occurrence as there are only about 250 marriages like this on record, and one of these couples gave birth to identical twin boys.
You may ask yourself, what significances this has in terms of DNA and DNA testing. Well, let me tell you. For starters, even though the offspring of a quaternary relationship would technically be considered first cousins, but their DNA would suggest that these first cousins were full genetic sibling. Since identical twins share the same genetic code, the four sets of DNA are really only like two sets. This makes it impossible to test the paternity of children from a quaternary relationship.
Additionally, children born to identical twins that are not married to or in a relationship with another set of identical twins would be considered half siblings, genetically speaking, as opposed to first cousins since two of the parents share the same genetic material. In this instance, it would be impossible to test the paternity if the fathers were identical twins because they share the same genetic code and there would be no way to determine which twin the child got his or her DNA from.
This can be quite confusing, so if you have any questions go to TestMeDNA.com for answers to all your DNA and paternity testing questions.