I don't think it's any typo (m)
I think it is a badly embellished form of Betsy. I'm only guessing, but it looks like it might be a Hispanic-style name. I see th used for the t sound in a lot of Hispanic names now, like Janeth and Arleth and Lizeth.
Betsy is very cute, but Bethzy, whatever its ethnicity, is just ugly.