For parents supervisa you need to be a pr or citizen and you will have less chances since you claimed asylum and they will think your parents will claim asylum as well
It is partially dependent on how long ago you received protected status, the current situation in their home country, whether they have strong ties to their home country try, etc. Your reason for needing asylum will also have an impact. If you applied for asylum because you identify as LGBTQ+ that reason for asylum is unlikely to apply to your parents so chances of approval would increase.