OSMANCIK, Turkey — In the hills of northern Anatolia, next to a shrine to a medieval Muslim mystic, there stands a modest building that illustrates the fears and frustrations of Turkey’s Alevi minority.

For years this small stone hall was a place of worship for local Alevis, heterodox Muslims who are estimated to form between a tenth and a fifth of the Turkish population. But one day in 2015, Ali Gormez, a local Alevi spiritual leader, arrived to find government officials had repurposed it as a mosque for the country’s Sunni Muslim majority.

Given that there was already a Sunni mosque a few hundred yards away, Mr. Gormez suspected the reasons for the conversion were not entirely benign. “The purpose was not to find another Sunni place of worship but to prevent the Alevis from worshiping as they like,” Mr. Gormez said during a recent interview beside the shrine.

“It’s a policy,” he added, “of denying the existence of Alevis.”

The political trajectory of Recep Tayyip Erdogan, the Sunni conservative whose Justice and Development Party, or A.K.P., has governed Turkey since 2002, is often judged through the prism of his increasing authoritarianismor by the challenges he is perceived to pose to Turkey’s secular traditions.

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