If you and her mother were not legally married at the time of her birth, it is not a guarantee that she automatically derived US citizenship at the time of her birth and, if not, then she is not eligible for N-600.  If you petition for her through I-130, however, you also have to be domiciled in the US; you cannot do it living in China for the entirety of the petition.  Furthermore, if you file and it is approved and she gets a visa, she does not get US citizenship but US permanent residence and in order to retain it and later gain US citizenship, she would need to be residing in the US.