With 32 voters on the roll at the 2023 parliamentary election, Yesilkaya stands 125th among the 127 localities of Kâhta, and its votes were cast at one ballot box.
The neighborhood parts ways with the district as a whole. At the 2023 parliamentary election it went to Yeniden Refah with 21 votes, while across Kâhta the leading party was AK Parti, with Yeniden Refah here running 63.5 points above its district average. In the presidential runoff, 33 of 35 valid votes went to Recep Tayyip Erdoğan — 12.9 points above the district average. At the 2017 referendum 37 of 37 valid votes were 'yes' — 15.8 points above the district average.
First place has changed hands 4 times here since 2009. At the 2024 local election the neighborhood went to Saadet Partisi with 15 votes, while Kâhta as a whole was won by AK Parti. Turnout at the 2023 parliamentary election was 96.9%, 11.6 points above the district average. At the 2024 local election Saadet Partisi and AK Parti finished level, on 15 votes each.