In a medium pot, combine chickpeas, sugar, cinnamon, allspice, salt, and water over medium-high. Bring mixture to a boil and cook, stirring occasionally, until sugar dissolves and liquid is very thick, about 12 minutes. Meanwhile, in a large skillet, heat oil over
medium (a chickpea should sizzle slightly when added). With a slotted spoon, strain off as much sugar syrup as possible, then transfer chickpeas to oil. Fry, gently shaking skillet to prevent chickpeas from sticking, until dark golden brown, 5 to 7 minutes. With slotted spoon, transfer to a wire rack set in a rimmed baking sheet lined with paper towels. Immediately season with salt; let cool completely.
Store in an airtight container at room temperature, up to 1 day.