Looking at the original you've linked, I see a name Hannah in the fourth line, but the word after that does not appear to be a surname, but rather the word "that," spelled "thatt." The following words appear to be "[thatt] if this Sd John..." The previous line appears to refer to begetting a Bastard Child, and the line above that appears to name John Thirber (possibly an alternate spelling of Thurber).
Maybe I'm misunderstanding. It might help if you posted your entire first draft of your transcription.