I wanted to find out when prophet Isa (as) was born and if there’s any books I can read about it.

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As far as i know we do not have a specific date of his birth. There are several good books i could recommend

https://www.amazon.com/Emissaries-Jesus-Shaykh-Rizwan-Arastu/dp/0692214119

https://www.amazon.com/Lost-Testament-Christians-About-Jesus/dp/0994240902

https://www.amazon.com/Jesus-Through-Quran-Shiite-Narrations/dp/1879402149