As general criteria (based on the police order), there is no seasoning period of 400K baht funds for a 1-year extension based on the parent of a Thai child.
But if I remember right, there are a few offices that require you to have your funds for two months the same as for an extension based on a spouse to a Thai.
I think Phuket doesn't, but you need to check with their policy in advance.
The easiest is going to international departure gate 2, there is a re-entry permit counter as the photo shows, before passport control, on the same floor (this photo was taken on 31 January 2024)