The court order the child to be put into temperary custody in the fathers house put the father might not be biological one but he's on the birth certififc. The mother is unfit

If the father is on the birth certificate he's the legal father. So the court is acting properly.

Who are you in this and what do you want to happen?

ANY question on law needs to include your general locale as laws vary by area.

The man listed on the birth certificate is the father and he will get custody if mother unfit.

Depending on location, if he is not the bio father, in some states (US)
1. bio father can challenge paternity but for limited time
2. bio father can challenge paternity

So this is correct and in most only the bio father can challenge this and in many places only for a limited number of months or years after birth

Also if they were married at the time of the birth then he is the presumed father and can legally sign the birth certificate. So just being the bio father wouldn't matter in a case like that.