Can a Nigerian National with a valid Schengen Visa visit Turkey?

Yes, a Nigerian citizen becomes eligible for Turkish e-Visa if he/she is holding a valid Schengen visa. Please note that there are some additional requirements. The website returned the following ones. I chose "Nigeria" and "Ordinary Passport" to see this list.

You must meet all the requirements listed below in order to obtain an e-Visa. Please confirm that you meet these criteria by clicking the boxes next to them. If you do not meet any of these requirements and you proceed with your application, your e-Visa will be invalid.

• I am travelling for the purposes of tourism or business.
• I have a valid Supporting Document (Valid visa OR valid residence permit from one of the Schengen Countries, USA, UK or Ireland). E-visas are not accepted as supporting documents.
• I have a round-trip ticket with Turkish Airlines, Pegasus Airlines, Onur Air or Atlasglobal Airlines.
• I hold a passport valid for at least 6 months from the date I intend to enter Turkey.
• I can prove that I hold a return ticket, hotel reservation and at least 50 $ per each day of my stay.
• I confirm that I meet each and every one of the conditions listed above.

This is an additional confirmation from Turkish MFA.

Nigeria: Ordinary, official/service passport holders are required to have visa to enter Turkey. These passport holders with a valid Schengen members or USA, UK, Ireland visa or residence permit may get their single entry e-Visas valid for one month e-Visas via the website www.evisa.gov.tr, provided that they meet certain conditions.

Diplomatic passport holders are exempted from visa for their travels up to 90 days.