What do you mean by type of infection?
The word "infection" refers to the invasion of tissues by pathogens, their multiplication, and the reaction of host tissues to the infectious agent and the toxins they produce. Infections pathogens could be bacteria, viruses, fungi, parasites, etc. Are you asking what type of pathogens could infect a wound on your hand? Or what type of bacteria, virus, etc.? What would do with the answer to the question? If you have bacterial infection, you're normally prescribed antibiotics, with no consideration (in the main) for what the bacteria actually is - because it (generally speaking) doesn't matter as you treat them in the same way.
If you're worried that a wound on your hand may have become infected, see your GP.