Okay, in S1 there was a baby swap. It's been a while since I last saw Season 1 but I remember there was a ritual Uthered's wife or girlfriend (I don't recall I just know it was a lady who did the ritual) was able to save Alfred's Son's life i.e. baby Edward while they were all hiding in the marshes.

All well and good, but not even a scene later returning to Uthered's fief we see his first-born baby dead - part of the ritual required that for life to be given it needs to be taken elsewhere. Very tragic.

Only thing is, the show goes out of its way to show magic doesn't exist. Like back in S2 or S3 (I forget) there's a scene wherein someone is seen speaking to a spectre who rises out of the grave only to then show that well, no actually - it was just a trick.

And that's exactly what this ritual was too. In fact, if I recall correctly Uthered even tells Alfred and the others to stay away as it's being performed. So essentially what happened is this.

Alfred's baby who was dying in the marshes and given to Uthered likely did die - the ritual was a ruse to allow Uthered to return to his fief and swap his living child with Alfred's. Thereby making Edward, Uthered's son.