The best replacement for jessie is jesse.

The best alternatives to jessie are rated as following:
★★★★★  jesse
★★  kickin it
★★  wheezy
★★  good luck charlie
★  angela
★  jake
★  misty
★  mixed chicks
★  austin and ally
★  seviper
★  jessy
★  shake it up
★  austin & ally
★  ant farm
  kaysha

Your alternative for jessie is not listed? Suggest!
Speaking about jessie, one probably shouldn't forget about austin and ally.

Other search terms related to jessie and their ratings are:
★★★★★ austin and ally
★★★★★ good luck charlie
★ good luck charlie christmas
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Google Trends

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jessie
jesse
kickin it