Must Zakat be paid in the month of Ramadan, or is it necessary to wait until next September if the first Zakat payment coincided with the month of September and Ramadan, then Ramadan advanced in subsequent years?

The lunar (Hijri) year is what is considered for the hawl (one-year period) of zakat (definition). Zakat must be paid immediately upon its due date, and it is not permissible to delay it except for a valid excuse. Therefore, it is not permissible to delay paying zakat until September (the solar month); rather, it must continue to be paid in Ramadan, along with seeking forgiveness for delaying the zakat of past years. The wealth must remain at the nisab (definition) (minimum threshold) for the entire year. If it falls below the nisab, the hawl is interrupted. The saved wealth must reach the nisab and a hawl must pass over it; merely receiving a monthly salary does not obligate zakat.