Hi, thank you for your question. Initially, you should formally write to the mother and request her agreement to undertake a DNA paternity test. If she refuses, you will then need to apply to court for a parentage declaration, the process of which you can find here:
If you do not have a birth certificate for the child, you will need to complete a further form C2 alongside the above application.
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How did you contact her two years ago? Have she moved away completely?