This is the türbe (mausoleum) of the saint.

Hacı Bayram-ı Veli (1352–1430) was a Turkish poet, a Sufi, and the founder of the Bayrami Sufi Order. He also composed a number of hymns.

Hacı Bayram, born in small village in Ankara province, became a scholar of Islam. He received instruction in sufism and became sheikh (leader) of an Islamic sufi order when his teacher died. He built a Dervish lodge on the site in Ankara where his tomb and mosque stand today. People came to stay there and learn about sufism. The Order grew popular with Bayram's successful teaching, and became known as ‘Bayrami’.

This growth perturbed some local authorities; they shared their worries with the Ottoman Sultan Murad II, who called Hacı Bayram to Edirne (the capital city at that time). The Sultan wanted to test the opinions, doctrine and (especially) the fidelity of the sheikh. At that time there were many independent Turkish clans in Anatolia, with very little unity among them.

Hacı Bayram took another scholar, his pupil Akşemseddin with him to Edirne. Sultan Murad soon understood that the complaints against Bayram were merely rumours, and Hacı Bayram and Akşemseddin stayed for a while in Edirne, lecturing and preaching to the court. He had private consultations with the Sultan and became his spiritual guide.
At Hacı Bayram’s request, his student Akşemseddin became the teacher of the imperial heir Mehmed (the future conqueror of Constantinople). Hacı Bayram made a few more trips to Edirne until he died in 1430 in Ankara, passing the leadership of his Order to Akşemseddin. His tomb and mosque in Ankara still attract many pilgrims.

Correspondent: J.M.Criel, Antwerpen.
Source: Wikipedia.