[LDS] members are encouraged to fast once a month on Fast Sunday and to give the money they save by not eating two meals to the church; those who can afford to be more generous are encouraged to give more than simply the money saved as a fast offering.
So given that the biblical root of the concept of a fast offering is the exhortation of Isaiah:
Is not this the fast that I have chosen? to loose the bands of wickedness, to undo the heavy burdens, and to let the oppressed go free, and that ye break every yoke?
Is it not to deal thy bread to the hungry, and that thou bring the poor that are cast out to thy house? when thou seest the naked, that thou cover him; and that thou hide not thyself from thine own flesh? (Isaiah 58:6--7)
And that Joseph Smith introduced the current LDS practice of using the cost of the meal foregone by fasting to support the poor in Kirtland (as later reiterated by the interregnal Council of the Twelve in these words):
Let this be an example to all saints, and there will never be any lack for bread: When the poor are starving, let those who have, fast one day and give what they otherwise would have eaten to the bishops for the poor, and everyone will abound for a long time; and this is one great and important principle of fasts approved of the Lord. (History of the Church 7:413)
Is there a separate modern root or inspiration of this practice? It doesn't seem to be derived from patristic or medieval Catholicism or Reformation practices as far as I know (which, admittedly, isn't a lot in the area of devotional practices). Specifically, was this something the Shakers, the Campbellites, or another Restorationist group influential on early Mormonism practiced?