Assalamu Alaikum, Is there any evidence that the polytheists (mushriks) lived under Prophet (pbuh)'s rule either by paying or not paying Jizya?
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If you mean by "polytheists" the idolaters, then we have not come across any evidence that shows that some of them were under the rule of the Muslims by paying tax or without paying it. As regards what happened with the Quraysh in Al-Hudaybiyah, then it was a truce and a treaty.
But if you mean the polytheists in general, including the People of the Book, i.e. the Jews and Christians, then it was reported that "When the Prophet sent Mu'aath to Yemen, he ordered him to take one Dinar from every pubescent person or its equivalent from Ma’aafir." [Ahmad, Abu Daawood, At-Tirmithi, An-Nasaa’i, Ibn Maajah]
Imaam Ash-Shawkaani said in Nayl Al-Awtaar: "Abu Daawood explained this narration by taking Jizyah from every pubescent person who did not embrace Islam. Also, Abu Daawood explained that Ma’aafir are clothes from Ma'aafir [a region in Yemen]."
It was also reported what proves that the Prophet imposed tax on the Christians of Daareen – in the vicinty of Bahrain. The book Al-Iktifaa’ Bima Tadhammanahu Min Maghaazi Rasoolu Allaah Wal Thalaathah Al-Khulafaa’ reads: “Ibraaheem ibn Abi Habeebah said: “Allaah turned the sea into a dry route for them ( i.e. Al-‘Alaa’ Ibn Al-Hadhrami and his companions) until they had traversed it over to them (the Christians of Daareen), and Al-‘Alaa’ and his companions crossed it by walking through it on their feet, although the ships used to cross it before and then the ships crossed it afterwards. They fought against them and Allaah helped them and they handed to him the Jizyah which they had refused to pay before, and which was set in the treaty that the Prophet had made with them.”
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