“There is no mitzvah to specifically give to any community or specific charity “
From mishnaic times through the period of the Rishonim (and possibly longer) there were mandatory community charity collections. See the last perek of Masechte Peah and Rambam Hilchot Matanot Aniyim. According to Rambam, who wrote that he had never heard of any Jewish community not having such an institution, anyone who refused to contribute the assessment could recieve lashes and have their property seized by beit din.