In the Qurʾānic verse in which fidyah is prescribed (Sūrat al-Baqarah, 2:184), no specific time is stipulated for its payment. Therefore, a person may give the fidyah at any time. This means that it may be given during Ramaḍān or after Ramaḍān.
However, since the time of death is unknown, hastening to fulfill one’s obligations and to perform good deeds without unnecessary delay is always the most appropriate course of action.