No, this isn't considered fee-basis income.
A fee-based public official is a person who receives and
retains remuneration directly from the public.
A person who receives payment for services from government
funds in the form of a wage or salary is not a fee-based public official, even
if the compensation might be labeled as fee.
For more information, please see the article on the Social
Security website, Fee-Based
Public Officials.
