If you wish to stay in Turkey longer than your e-Visa permits, you must apply at local Police Station for a residence permit. Please note that an e-Visa is granted only for tourism and trade purposes.
Application for other types of visa (work visa, student visa etc.) are required to be submitted at Turkish Embassies or Consulates. If you overstay your visa, you might be asked to pay fines, deported or banned future travel to Turkey for a specific period of time.