How could I scientifically explain a world with day/night cycle only on the equator?

I'd like to build a world that has one pole where it's constantly day (all year long) and the weather is very hot, and one where it's constantly night (all year long) and the weather is freezing.

I'd like for the area in the middle, especially around the equator, to be more temperate and have a day/night cycle of sort (most settlements would be there).

Is there a way to explain it scientifically, maybe through the positioning of multiple stars or other celestial bodies?

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How could I scientifically explain a world with day/night cycle only on the equator?

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