Is there a legally mandated filing fee and/or deposit?

Ireland

Answer

Yes, deposit

Source

http://www.irishstatutebook.ie/1993/en/act/pub/0028/print.html

Presidential elections act, 1993

PART V

Presidential Election Petitions

(4) A petition shall bepresented by being lodged in the Central Office of the High Court not laterthan 3 days after the grant of leave by the High Court under subsection (2) but a petition (other than a petitionby the Director of Public Prosecutions) shall not be accepted in the CentralOffice unless the petitioner lodges in the Central Office with the petitionsecurity in the sum of ?5,000 (or such lesser sum as that court may considerappropriate if it is satisfied that such lodgment of ?5,000 could not be madeby the petitioner or could cause him serious hardship) for any costs of theproceedings in relation to the petition which may become payable by thepetitioner.