If you go to https://www.evisa.gov.tr/en/apply/ and enter your intended date of arrival in Turkey and your travel document type, and then proceed to the next but one page, you will be presented with a dialogue box which says:
- 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.
Five criteria are listed, including being below 20 or over 45 years old; or holding a valid Supporting Document (Valid visa OR valid residence permit from one of the Schengen Countries, USA, UK or Ireland).
The FAQs https://www.evisa.gov.tr/en/info/ state:
“The only requirement for your visa/residence permit to be used as a supporting document is that it should be still valid (by date) by the time you enter Turkey. Previously used or unused single-entry visas are accepted as long as their validity date covers your entry date to Turkey. Please note that e-Visas of other countries are not accepted as a supporting document.”
Therefore, you are eligible to apply for an eVisa for Turkey with your used single-entry Schengen visa provided you enter before 7th September AND you can confirm that you meet the other criteria.