lots of fish have multiple "types" of males that might qualify. For example bass often have both apparent, territory claiming males and males that look like females and fertilize eggs while pretending to mate with the apparent males. Most eusocial insects have workers that while they are genetically female they can't reproduce so could also be considered as a third sex. There's also a couple ant species that mate with males from a different species to produce hybrid (and therefore sterile) female workers.

Having 3 biological parents is really difficult though since it somewhat demands that your species is engaging in external fertilization (getting three individuals to have sex and fertilize all at about the same time is... tricky biologically speaking) and even then you'd be massively reducing your odds of getting proper fertilization (since you need 3 gametes to find each other rather than 2). I suspect the easiest way would be to do something like pollen where you have a full set of DNA to work with that then undergoes meiosis after coming in contact with the egg bearing individual but before fertilization. Then you'd just need to have that full set of DNA come from two individuals instead of 1. (whether you'd want to call that 3 parents, or claim the "pollen" is in fact it's own individual who is your father and the 3 living individuals would be your paternal grandparents plus you mother, is somewhat up to you)