Essentially this.
However, I do suspect the mother not to be Swiss (because of the mention “2 years on the territory”) and this is where things can get a bit complicated, because of the potential foreign legal implications.
I found several government links – but unfortunately only in German, French or Italian:
Child recognition by the father: https://www.bj.admin.ch/bj/de/home/gesellschaft/zivilstand/faq/kindesanerkennung.html
And some legalese – if you really want to dig into the matter an know your rights (unfortunately all in German) – both are PDFs below:
Business case: Recognition of children in Switzerland and abroad https://www.bj.admin.ch/dam/bj/de/data/gesellschaft/zivilstand/weisungen/prozesse/33-1.pdf.download.pdf/33-1-d.pdf
Certification of the birth of a child of foreign parents whose data cannot be found in the civil status register https://www.bj.admin.ch/dam/bj/de/data/gesellschaft/zivilstand/weisungen/ws-ks-am/20-08-10-01.pdf.download.pdf/20-08-10-01-d.pdf
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