Hm.. what is the definition of twins here? If the definition of twins here is that the mom gives birth to them at one shot, then ya, it is possible for twins to have different father. Of course the mother would have to be seeing two men at the same time.
On the other hand, genetically speaking, identical twins come from the same ovum and same sperm which means they look alike and share the same sex, whereas fraternal twins come from different ovums and different sperms which could allow them to look different and have different sex. The possibility of having different fathers in the second case is possible, at least in theory. I'd like to see that in reality though.