While making Wudu during fasting, what is the procedure for rinsing the mouth? If we swallow water by mistake, is the fast void?

Praise be to Allah, the Lord of the Worlds; and may His blessings and peace be upon our Prophet Muhammad and upon all his Family and Companions.

A fasting person is required to be careful to keep his fast valid and avoid all that could nullify his fast. The way of rinsing one's mouth is the same for a fasting and a non-fasting one. But the fasting person should avoid drawing the water deep into his nose. The Prophet (Sallallahu Alaihi wa Sallam) said: "Exaggerate when rinsing your nose unless you are fasting." [Reported by four Imams of Sunan].

However, if the water reaches into the throat or stomach unintentionally or due to forgetfulness, it does not affect the fasting. The Prophet (Sallallahu Alaihi wa Sallam) said: "Whoever forgets he is fasting, and eats and drinks is to complete his fast, as it was Allah who fed him and gave him something to drink." [Reported by Imams Al Bukhari and Muslim]. If one does so intentionally he commits sin and has to make up that day later.

Allah knows best.