Since You said parrotfish, which are really a saltwater fish, and the fact that parrot cichlids are not that common, and you said you heard they might not be fertile, I am going on the asumption you mean Blood Parrots(3 different fish there, parrot fish=SW parrot cichlid=pure natural strain, blood parots=hybreds). Hybred fish that do produce offspring often have many genetic deformities, so be prepaired to cull(nice word for kill) any fry that are in poor shape.
Most parrots are infertile. However some can produce offspring. Look for eggs that have turned white, this means they will not hatch. If you have healthy eggs (the odds are against you) It is your choice to let the parents try and raise them(most cichlids will take a try or 2 before they get it right) or remove the eggs to another tank. If you remove them, they will need excelent water quality and good filtration, with something blocking the filter intake, such as a sponge, to keep the fry from being sucked up.