Hi Vineet, You can apply for an e-Visa for Turkey, only if you have any valid visa or resident permit from the US/UK/Ireland/Schengen states. If you have a valid tourist visa, residence permit, work permit, or permanent residence in any of these countries, you can apply for a Turkey e-Visa online and fly right after.
So, if your Schengen Visa has expired you need to apply for it again. You can double check this from the right authorities by writing your query to info@schengenvisa.cc