My uncle told me that his grandmother (my great-grandmother)'s first name was Jessie
The name Jessica or Jessie/Jess in Polish is Dżesika (pronounced same as Jessica).
The Polish form appeard in Poland not long ago, just in '90.
There is no Polish equivalent to name Jessica, just a made up Polish form Dżesika
, which officially can be registered in Poland as a first name.
When you look at the name's origin, Jessica is of Hebrew origin, more here: thinkbabynames.com/meaning/0/Jessica
could Jessie or Jesse be an 'anglicized' nickname for Czesława? Or if not what would be an equivalent Polish name that I should be looking for?
I forgot to add some more.
No, Czesława could not be Jessica or Jessie. Some of Czesława forms are: Czesia, Cześka. sometimes Sława.
There is one female name Janina
(Engl. Jane) which could end up in English version as Jessie/Jesse because one of deminutives of Janina is Jasia
, a little bit like Jessie.