Acquisition and derivation
Some people acquire citizenship at birth abroad through a citizen parent, subject to the parent's own residence or physical presence in the United States before the birth. Others derive it automatically as children, when a parent naturalises while the child is a minor, a permanent resident, and in that parent's legal and physical custody.
In both cases the person is already a citizen. Nothing further is applied for; the N-600 simply documents what is already true.
Which law applies to you is a question of dates
This is the part that makes these cases technical. The rules have changed repeatedly, and the version that governs is the one in force at the relevant time — your birth, or the date the conditions for derivation were met. The Child Citizenship Act of 2000 changed the landscape for many people, and did nothing for others born a few years earlier.
The right answer depends on your date of birth, your parents' marital status at the time, their immigration history, and dates of physical presence that often have to be reconstructed from old records.
Certificate or passport?
A United States passport is also evidence of citizenship, is cheaper, and usually comes faster. The certificate is permanent documentation that does not expire and is often the cleaner proof for employment, benefits and the record of your own children's claims.
Many people get both. If you only get one, which to choose depends on what you need it for.
Questions we are asked about this
I have lived here since I was a child and my mother naturalised. Am I already a citizen?
Possibly, if you were under 18, a permanent resident, and in her legal and physical custody when she naturalised. People discover this at the worst moments — sometimes in removal proceedings. If it might apply to you, it is worth checking now.
Is there a deadline to file an N-600?
No. Citizenship you hold does not expire, and the certificate can be applied for at any age.
Can I file for my child?
Yes, a citizen parent can file on behalf of a minor child. There is also a separate process for certain children living abroad.