His existence is proposed on the details of a legend in Safvat as-safa, a work by Ibn Bazzaz who mentions Akhsitan as ruler of Shirvan.
[1] According to legend, Shah wanted to marry his daughter to Safavid sheikh Safi-ad-din Ardabili with a dowry of 14,000 dinar and a water canal, to which Safi al-Din reporedly replied "How can I reply to that?
Since Safi-ad-din Ardabili was born in 1252, he couldn't have married a daughter of Akhsitan II, about whom after 1260, there is no details.
According to the legend, seeing Safiaddin's tutor and future father-in-law Zahed Gilani's influence over Shirvani people Akhsitan began to oppose religious Sufi orders, saying religious people are not working in fields.
[1] Another reasoning given for his existence is an inscription dated June 1294 on Pir Huseyn Khanqah, which mentions "Keykavus b. Akhsitan".