I don't like the name Jessie, and I think that Jessye is even worse. However, if you like this name, give it to your child. There isn't anything wrong with it. You don't have to agree with my opinion though. :)
And for my opinion, I think this is probably kept as a nickname in the youth. If you like this, you'd probably be better off calling your daughter Jessica, then stylising "Jessie" in this way. But, she'd probably grow out of "Jessye" eventually.
Jessye? Really? Ugh, this is more stupid than Rubye! It looks like Jess-EYE, or rather "Jess! Bye!" Thankfully, (and I know a few Jessica's), I don't know anyone who uses this spelling, which means it's not common. I hope it stays that way.
Looks like JES-sye to me. Come on, this is a silly spelling of an infantile name that works as a nickname, but sounds childish as the actual name of an adult.