supplemental ticket; hand-written ticket
A ticket issued manually, often by train station staff, to supplement or replace a regular ticket when the ticket machine cannot issue the desired fare or route.
The station staff issued a hand-written supplemental ticket for me.
For tickets that cannot be purchased at the automatic ticket machine, please get a supplemental ticket at the counter.
Compound of 補充 (supplement, replenish) and 券 (ticket). The term likely originated in railway contexts where staff needed to manually issue tickets to supplement machine-issued ones.