There is no such thing as paternal twins, only fraternal and identical twins. Fraternal twins develop when two separate eggs are fertilized, while identical twins develop when a single fertilized egg splits into two.
Fraternal twins result when two different eggs are fertilized by two different sperm in a single pregnancy. Despite developing and being born at the same time, fraternal twins are no more genetically similar than any other set of siblings. Fraternal twins are equally as likely to be the same sex or opposite sexes.
Identical twins, sometimes mistakenly known as paternal twins, result when a single fertilized egg splits into two separate embryos. Identical twins share the same set of DNA and, thus, are always the same sex unless there is a mutation during development. Despite having identical DNA, these twins do not always appear exactly the same. This is because many physical features are influenced as much by the environment as genetics. For instance, one twin might weigh more than the other. Even fingerprints have an environmental component to their development; identical twins share very similar fingerprints, but they are not an exact match.
There is a rare third type of twin: polar body or semi-identical twins. These twins share the same DNA from their mother, but have different DNA from their father. The exact mechanism by which this occurs is not fully understood.