According to King Herod's Dream: Caesarea on the Sea the Muslim Turks who settled in 1882 were given land by the Ottoman Empire as refugees from Bosnia. Bosnia and Herzegovnia fell under Austro-Hungarian rule in 1878 at the Congress of Berlin following the Russo-Turkish war. There was a subsequent uprising in 1881-1882, nominally against the imposition of Austrian military service requirements. There were less than a hundred Bosnian Muslims who settled on the site of Caesarea and most likely were forced into becoming refugees by the turmoil in the area. Many "Bushnaks" or Bosnian Muslims settled in Ottoman Syria in that time, fearing Christian rule following the Austrian annexation.

The Bosnian refugees laid out a small town (Qisarya) within the ruined crusader fortifications and included "streets, alleys, a bakery, several mosques, and the house of a Turkish mudir ('governor')." They farmed and sold stones quarried from the ruins as building material.

Later on, however, in the early 20th century, Baron Edmond de Rothschild of the French branch of the family purchased a concession from the Turkish sultan for land between the Crocodile River and Hadera River, which seems to have included the site of Caesarea. He founded a company called the Palestine Jewish Colonization Association (PICA), which (according to King Herod's Dream) purchased the Bosnian holdings. Historical records from the Jewish Daily Bulletin show there was considerable tension between PICA settlers and local "Arabs" in the region at least as early as the 1920s.

On May 2, 1940, Jewish settlers from Haifa established Kibbutz Sdot Yam on the site of Caesarea. Bosnians lived on the site until 1948. Many Bushnaks assimilated into the local Palestinian population in the aftermath of the 1948 Arab-Israeli War, but I have no specific data on the fate of the Bushnaks of Qisarya.

Sorry for the late response, I meant to answer this question earlier but forgot.

Also: the details of my answer with respect to Bosniaks of Caesarea in particular will largely be based on this 1981 anthropological study of the community by Nina Seferović. So if you have some further questions I would implore that you look at that article first.

So let's start off first with the question of why Bosnian Muslims would settle in Palestine. In 1878 the Ottoman Empire was compelled to comply with the treaty of Berlin which would partition its Balkan territories between a number of states and would lead to a large number of Muslims emigrating from the new states that they found themselves in back into the Ottoman Empire. The reason for this varied; many Muslims lacked political and social rights and were discriminated against under these new regimes, while others migrated for more personal reasons or simply for the desire to live in a Muslim state.^1 In Bosnia, it seems the reasons largely consisted of the latter type, but after 1881 there was also another wave of migration largely in response to a new conscription law implemented. The total number of migrants from Bosnia is disputed,^2 but the generally accepted number is a roughly 60,000 person net emigration from Bosnia (or roughly 10% of the Muslim population of the time). With regards to the the Bosniaks of Caesarea in particular, Seferović puts the number of emigrants who settled at Caesarea at around 100 families who migrated largely out of fears and the uncertainty of their lives under Austrian rule.

The resettlement of migrant populations was a matter that was generally decided on both on the level of the 'individual' migrant and also on a state level. During the late 19th century the Ottoman Empire generally followed a policy of wanting to settle migrants into the frontiers of the Empire to try and exert more control over these areas. This might manifest in trying to make certain areas more demographically Muslim in character, or in some areas like Libya,^3 Syria, and Eastern Anatolia there were also efforts to diminish the influence of tribes and populations thought to be unruly. Still we should not make the mistake of erasing the influence and views of the migrants however, as there was also quite a bit of evidence to suggest that migrants had their own choices of when and where to migrate. Many migrants did in fact decide for themselves where to settle, with some making the decision to resettle from places where they had been allotted and some even returning back home. In the case of this particular Bosniak community, they originally set out to Syria because they believed "that they would find greater religious purity while living in the ancient Islamic lands" and thus settled near Damascus. They did so with no government direction and aid as well. However, after facing increasing hostility from local populations who perceived them as foreigners they petitioned the Ottoman government for their aid in order to be able to settle on the ruins of Caesarea in Palestine. The Ottoman government agreed to assist their resettlement and most of the Bosniak community moved into Caesarea (leaving only a few families behind in Damascus).

The newly found village was small but still fairly sustainable, they were also well off enough to employ local farmers (fellahin) to cultivate their lands. The location of the city with its port, made it a pretty important settlement for the local economy as well. It was organized according to standard Ottoman law at the time and was not isolated either, the village had good relations with nearby Jewish populations, and they also employed an Arab scholar as a teacher and imam of their mosque. Other migrants; from the Balkans and the Caucasus also continued to arrive in the village over time, and new arrivals continued to come well into the 1930s which included many women who were brought in from Bosnia as wives.^4 In particular Seferović points out the continued use and knowledge of Bosno-Serbo-Croatian among the community well into the 1930s and 40s which was a result largely of the women of the community who preserved its usage.

Emigration from the Caesarea village into other areas of Palestine and Syria also occurred and especially for the purpose of pursuing an education as the village only had a primary school. Later the influx of German and Jewish migrants and the economic decline of the village as a result of the increasing prominence of the port in Haifa would result in even more Muslim emigration from village. Even still there continued to be Bosnian families who continued to live in the village of Caesarea until 1948.

In 1948 the remainder of the village (as well as many of those Bosnian families who still lived in Palestine), like most other Palestinians were driven from their homes. Today descendants of that Bosniak community in Palestine still exists with most living outside of Palestine (i.e. in Jordan, Lebanon, other Arab countries, and some in Turkey as well) but aside from certain markers of their heritage (like the name Bushnak) there are no longer any discernable differences between them and the rest of the Palestinian community at large.

Sources:

• Blumi, Isa. 2013. Ottoman Refugees, 1878-1939 : Migration in a Post-Imperial World. London ;: Bloomsbury.

• Clayer, N., Bougarel, X., & Kirby, A. (2017). Europe’s Balkan Muslims : a new history. C. Hurst & Co. Publishers Ltd.

• ŞENIŞIK, PINAR. “Cretan Muslim Immigrants, Imperial Governance and the ‘Production of Locality’ in the Late Ottoman Empire.” Middle Eastern Studies 49, no. 1 (2013): 92–106.

• Seferović, N. (2015). The Herzegovinian Muslim colony in Caesarea, Palestine. Journal of Palestine Studies, 45(1), 76–92.

• Şen, Bayram. 2014. “SHUTTLE BACK AND FORTH BETWEEN TWO EMPIRES: THE PETITIONS OF BOSNIAN MUSLIM MIGRANTS IN THE OTTOMAN AND AUSTRO-HUNGARIAN ARCHIVES AT THE END OF THE NINETEENTH CENTURY.” Prilozi Za Orijentalnu Filologiju, no. 64: 325–44.

Notes:

1. Traditional Islamic Legal thought of the time generally expresses a preference for Muslims to live in a state ruled by Muslims even if they would be allowed to practice their religion freely in a non-Muslim state. Still we should be careful not to emphasize this point too much, local Ulema in Bosnia issued fatwas encouraging Muslims to stay in Bosnia as freedom to practice Islam was still guaranteed, and Muslim reformers like Rashid Rida also wrote to encourage Bosnian Muslims to stay in Bosnia.

2. The issue is that migration wasn't really a one way street; while most Bosnian Muslims remained in the Ottoman Empire, there was quite a large portion that returned back to Bosnia for various reasons, and some Bosnian Muslims even moved back and forth between Austro-Hungarian Bosnia and the Ottoman Empire constantly. For this reason many scholars suspect that the actual number of Bosnian migrants into the Ottoman Empire was lower than what was once thought.

3. Pinar Senisik in "Cretan Muslim Immigrants, Imperial Governance and the 'Production of Locality' in the Late Ottoman Empire" demonstrates how Cretan Muslims were settled in Cyrenaica to curb the influence of the Senussi order in Libya for example.

4. The community, according to Seferović, tended to be endogamous, with preference being marriage from within the Bosniak community of Caesarea and also with Bosniaks from the diaspora in other places like Turkey as well. Intermarriage with Arabs also occurred especially after the first few years of the settlement when disease, and sterility had hit the community quite badly.