How much does it cost for everything to file a petition for correction of entry for birth certificate?

I want to file a petition for correction of entry of my daughter's birth certificate and i want to know if anybody who already done this or experience this or anybody that could help me to give me an idea of how much money should i prepare to get this petition done. some people said that to file a petition wouldnt be that much, but the lawyer would be expensive...any information about this, i would really appreacite. thank you