In the An authentic narrative (published in 1772) is a list of the Turkish fleet (p. 17) published, just before the battle with the Russian fleet. See also this weblog the notes dealing with the sea battles between the Russian and the Turkish navies as reported by the Dutch ambassador at the court at Constantinople .
“The Capatana Hali Bey. 100 guns
The Capatana Bacha, 96 guns
The Catrona Aucharee, 84 guns
The Reala Mustapha, 84 guns
The Mulenso Achmet, 84 guns
The Zefir Bey, 80 guns
The Achmet, 74 guns, burnt with the Emir Mustapha, 7 frigates and several gallies and zebecs
The Emir Mustapha, 70 guns
The Hamesi, 60 guns
The Barbaroscena, 60 guns
The Hali Condicta, 60 guns
The Meehin, 60 guns
The Repulin Bacha, 60 guns, tajen with four half gallies and barges
The Rhodes , 60 guns
Total of the line of battle ships 14
Two large frigates, some smaller, three whole gallies, many half and quarter gallies, besides zebecs,&c.
These, together with the traders and neutral ships burnt in the harbour of Chiesma
Source
An authentic narrative of the Russian expedition against the Turks by sea and land containing every material circumstance of their proceedings from their first sailing from Petersburgh to the destruction of the Turkish fleet, in the Archipelago. London
