Twins are defined as "...two young who are simultaneously born from one mother." (Encyclopedia Britannica). Note that the definition only refers to the mother. But what about fathers?
As technology has improved the accuracy and accessibility of genetic testing, it has become more evident that twins can have two different fathers. The situation only applies to fraternal (dizygotic) twins, not identical (monozygotic) twins, which form from a single egg/sperm combination.
However, fraternal twins are the result of hyperovulation, the release of multiple eggs in a single cycle. Superfecundation describes a situation where the eggs are fertilized by sperm from separate incidences of sexual intercourse. In a case where a woman has sex with different partners, the twins could have different fathers. The appropriate term to describe this situation is heteropaternal superfecundation.
This situation can also occur when twins are the result of fertility treatments, for example the case of Koen and Tuen Stuart, Dutch boys who were the result of IVF (in vitro fertilization). In a mixup at the lab, equipment had been used twice, causing another man’s sperm to be mixed with the father's.