That top looks like a YJ top. I have a 1990 Yj and like your doors, the edge of the soft window is flush with the edge of the half door, but mine came with a soft top originally. I think if you had the hardtop option from the factory your doors would have the notch cut out for the top. You may be able to use the upper doors from a '97-'02 TJ to fit the top, but I don't know if they would fit your doors. I'm not sure if the YJs had a hard top/half door option.
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