See link below
If you are seeking a Paternity Judgment, commence a Paternity Action with a FL-200 Petition to Establsh Parental Relationship.
Please note that this answer does not constitute legal advice, and should not be relied on, as each situation is fact specific, and it is not possible to evaluate a legal problem without a comprehensive consultation and review of all the facts and court pleadings filed in the case. This answer does not create an attorney-client relationship.
To obtain a court judgement establishing parentage, you would need to file the proper paperwork with the county court, usually where the child lives, including the FL 200 as Mr. Conviser mentioned. You did not say whether the father would dispute his paternity or not. Filing the paperwork gives the alleged father an opportunity to respond and dispute paternity if that is his position. He could request a DNA test as part of this process. There are Self-Help Centers in the courthouses to help you with the forms. Additional information can be found at: http://www.courts.ca.gov/selfhelp-parentage.htm. You'll see that on the FL 200, you will also need to answer questions about what type of custody and visitation arrangement you would like.
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Diamond Tran, Esq.
This is not legal advice and this response does not create an attorney client relationship between this office/me and an other person or entity.
I have linked the documents you will need.
Form FL-200 is the main document you are looking for.
The second linked document, FL-105, must be completed and filed with the FL-220.
The third linked document is sometimes required depending on your situation, so please see if FL-105(A) applies to you and yours.
The final linked document below be filed at the same time as FL-200, but do not fill it out (leave it blank). Good luck!