Your browser may warn you that this is not a trusted source. It did warn me, but I went ahead and used the source with no problems. (Apparently, they are in the process of obtaining a new security certificate, and the issue should be resolved soon.)
On this site, you can search manuscripts in Turkey, see some of them online, and even order digital copies of pages, paying a certain amount per page with the credit you purchase with your credit card online. I believe the search function is open to all -- you do not have to be a member to the site. You just have to make sure that you can use Turkish letters in your browsing software so that you can enter the right diacritics for modern Turkish (circumflexes do not seem to matter). After you enter a search term, like the author "Mustafa Ali,"
you get to a page where all the relevant manuscripts are shown to you by name, call number, etc. On that page, on the right hand side there is a column called "G." If you see an eye on that column, you can actually view the manuscript online (click on the call number, then scroll down on the next page and select a page from the thumbview) -- but only if you get a membership. After you get a membership, the page you see will have the logo of the Turkish Ministry of Culture in the center. But if you purchase some credit and "buy" a digital copy of the page, the copy you download comes without the watermark logo.
This is a database of articles on Islamic Studies published in the circles of Theology Faculties in Turkey. Once you click on "arama sayfasi" on the upper right corner, you get to the database search page. I just tried the keyword "osmanli" [with an I, though, that is an "i" without a dot] and got 183 entries for many of which the database includes a pdf copy of the relevant article (the announcement page states that they have 15,000 entries and 11,500 pdf documents).
Middle East & Islamic Studies, http://www.library.cornell.edu/colldev/mideast/