To get to the luggage belt, you need to leave the secure area. As per the Frequently asked questions
If you will not leave the transit lounge at the airport you are not required to have transit visa. Otherwise, you have to make visa application to the nearest Turkish Representation.
Ie. there is no separate transit visa you could get.
While I obviously can't know, I will presume you are holding an Indian passport. (Source). According to the Visa Information For Foreigners page
India: Diplomatic passport holders are exempt from visa for their travels to Turkey up to 90 days. Ordinary, Special and Service passport holders are required to have visa to enter Turkey. Ordinary, Special and Service 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 via the website https://www.evisa.gov.tr, provided that they meet certain conditions.
so there. If you have a visa to any of the listed countries then an eVisa is now available, this was introduced last fall. Otherwise, you need a "sticker visa" ie one you apply for at the embassy and get affixed into your passport.