@KnezIvan  Most Bosniaks might be ‘just Serbs’ historically like @Knez said (That’s a lot of knezevi lol) but not exactly in the way he thinks. I don’t know why, but most people think that Christian Bosnians suddenly converted to Islam in masses. Definitely not true. A lot of the ancestors of the modern day Bosniaks were converted Muslims already from mostly Serbia (Serbia saw a lot of converts in a relatively short time) but also Croatia (the exodus of converted Muslims after the AH took over northern Croatia), Bulgaria, Macedonia, Albania, and smaller quantities from other places. Bosnia’s Ottoman demographic was severely changed from a sparsely populated medieval Kingdom to a far more densely populated Ottoman territory with huge chunks of it’s population imported from the Ottoman Empire (mostly from neighboring Balkan regions). 
Most historians agree that medieval Bosnia was a nominally Catholic kingdom. However, there was a Christian sect within Bosnia (previously thought to have been “Bogomil” but most historians today agree it was a Catholic derived sect) and a lot of the Bosnian nobles belonged to this sect. There was also an Orthodox presence on the eastern frontiers of the kingdom that bordered Serb lands.  When the Ottomans invaded a lot of the Catholics fled to to Hungary-Croatia and Catholic Europe or they huddled in Franciscan run villages. A lot of the Bosnian Christian sect members in the noble class converted to Islam to keep their property and other rights. When the Ottomans conquered most of Croatia for over 100 years some portions of Croatia were Islamicized, particularly in Slavonia. When the Hapsburg Empire conquered northern Croatia from the Ottomans a lot of the converted Muslims there fled to Ottoman Bosnia while Catholics from Bosnia again fled to Austrian lands (a lot to Slavonia like a population exchange). Virtually all traces of Islam were wiped out in Northern Croatia but vague reminders of it can still be found.  
By far though, some of the most influential Slavic speaking Muslims in Bosnia can trace their roots to Serbia and to the south East. The heart of the Serbian kingdom, Raska, saw pretty large scale conversions to Islam of its original Serbian Orthodox population. This land was known as “Sandzak” in the Ottoman Empire and was made a single administrative unit with Bosnia. Southern Serbia in particular saw a lot of Islamification partly due to conversions of Serbs but also due to converted non Serbs settling their lands (i.e. the first Islamic Albanians-Arnavuts in Kosovo). A lot of these people in Serbia moved to Bosnia while a significant chunk of the Christian population moved to Austria-Hungary (hello Vojvodina and Vojna Krajina) after AH had some successes in a few battles. Even Bosnia’s most famous president, Alija Izetbegovic, can trace his ancestors originating from Serbia. 
So yeah, all in all I’d say a good portion of today’s Bosniaks probably can trace their roots to Orthodox Serbs. This is certainly evident culturally since most parts of Bosnia are far more similar to Serbia than Croatia (they developed culturally together in the same empire for centuries) which makes them kind of like sister nations raised by a Turkish grandfather :P. As concerns the medieval Bosnians, well most of them fled the country while upper class ones converted and kept some of their prestige, or their remnants can be found mostly (but not exclusively) in the Catholic population that remained.