Proper designation of this rifle is an 1888/35.
It started off as a Gew. 88, went through the S, Z and '14 conversions, then was sent, likely after service on the Western front, to Turkey.
The majority of captured Turkish rifles during the war were stacked in piles by the British and set alight. The Brits did this through the Palestine campaign because they did not have enough troops to take and guard a zillion prisoners and still fight a war. The decision was taken to turn Johnny Turk loose to find his own way home, but to police up all the rifles from the battlefields and destroy them. I had this personally from Bty/Sgt Angus Kellie, 520 Siege Bty, RA. Sgt. Kellie served in the Middle East from 1915 through 1921, fought at Suez, Gaza, Beersheba, Jerusalem, Armageddon and right to the end of the campaign.
When the war was over, all Turkey had remaining were some Peabodies, 1871/87 Mausers, 1890s, 1893s, 1903s, Gew 98s, Gew 88s in SZ'14 configuration (standard and nm types mixed). When it came time to do something with this dog's breakfast of weapons, the decision was taken to get rid of the old Peabodies and 71/87s, being that they could not handle modern ammunition pressures. The 1890s, 1893s, 1903s all were in calibre 7.65x54 and many were pretty ratty. It was an easy job for Turkey's nascent gunmaking industry to ream these and convert them to 8x57.
88s and 98s already were in 8x57, so barrelmaking machinery was obtained and the changeover began with a massive cannibalisation of what they had. As to 1888s, as many as possible were rebuilt with cannibalised parts, some new barrels made. Surplus 1888 actions were set in new stocks made from Turkish Walnut and fitted with heavyweight 8x57 barrels. That is what your rifle is.
I have one and, as so many have stated before, it is a beautiful shooter. That heavy barrel really anchors thing nicely, even if it would be a bit of a chore to cart it around.
You have a very real piece of history there! Treasure it, load for it, have fun with it!
Late at night, if you listen carefully, it might tell you about what Liman von Sanders had to say..... or about the time it almost met Lawrence.
It was there; it is The Real Thing.