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If you are certain that the child does not qualify for any nationality resulting automatically from his birth then the only conclusion to make is that he is stateless.
On this basis he is born outside the UK to a british father and he is stateless.
However, being stateless does not nescesarily mean that you MUST appy using form s2 (although you probably could if you wish it would take longer than using form MN1).
For this reason I would personally apply using form MN1. You will see that the third paragraph under the heading s3(2) at page 9 of the guidance confirms that the 3 year residence requirement does not apply if the child is stateless and so this is effective confirmation that you can apply using form MN1 even though the child is stateless:
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I'm afraid that I am unsure on this point, you can certainly express the urgency in the covering letter to the application in the hope that they will expedite it...Tom