Do you mean slaves of Arab descent or slaves taken by Arab traders? If you mean people of African origin, then the answer is, there are most definitely groups descended from slaves. If you mean within North Africa and the Middle East, that is less an area of study for me, but I'll see what I can do at the end of this post.
In India, there are the Siddhis, who are the descendants or partial descendants of sub-Saharan Africans traded from the Arab Peninsula all the way to India. Shihan de Silva in "African Identity in Asia: The Cultural Effects of Forced Migration" has charted different rituals and folk traditions, linguistic markers, and dance and musical traditions to show Siddhi influence from Yemen to the Deccan Peninsula.
Portuguese and Dutch sources in the Indian Ocean often remarked on the military and seafaring prowess of Siddhis. Indian kings and Shahs used Africans as cavalrymen, bodyguards, generals, and soldiers, citing their lack of familial ties as a true loyal bond.
Some, like Malik Ambar, ended up being powerful enough to control kings and depose one that slighted him by not wanting to marry his daughter. The states of Sachin and Janjira actually survived Mughal invasion somewhat intact, and lasted through British colonial control, and both of those states had descendants of the Siddhis.
Note, in different source text, you may also see the word "Habshi" or "Habash" instead of Siddhi. Most of my area of study here is on the African Diaspora, so if your question is more on slave enclaves in North Africa in the Middle East instead of African descendants moved around from the diaspora and slave trades, then let me know.
Within North Africa, Mauritania may be closer to what you are looking for. Khaled Esseissah in "Paradise is Under the Feet of Your Master: The Construction of the Religious Basis of Racial Slavery in the Mauritanian Arab-Berber Community," asserts that slavery still exists in a racialized form in Mauritania and the issue is downplayed by the current government. Esseissah points out that modern race relations, economic and political institutions and rights even today show that racial splits passed down and inherited from the earlier slave trade. This may be more your question, and answers with an affirmative.
If you have other questions let me know, this may have been disjointed, but these two examples sprang to mind.
Sources: African Identity in Asia: Cultural Effects of Forced Migrations by Shihan de Silva Jayasuriya (a great primer how the African Diaspora affected Asia, with a lot of interesting linguistic and anthropological data mixed in)
Islam's Black Slaves: The Other Black Diaspora by Ronald Segal (background material and reference)
Khaled Esseissah - "Paradise is Under the Feet of Your Master: The Construction of the Religious Basis of Racial Slavery in the Mauritanian Arab-Berber Community" - This may be more your jam and shows that these ethnic groups and their modern descendants definitely experience racial differences and discrimination in the modern day.
There's a section on this in the FAQ if you want to read two past threads on this topic:
To clarify, what do you mean by “no major ethnic groups”? There are populations of Afro-Arabs spread throughout North Africa and Asia, but their histories and political status does vary country by country. Just as an example, there are 1.5 million Afro Arabs in Iraq.
Are you asking why they remain small compared to descendants of the trans-Atlantic slave trade?
There was a comment about the Siddi population in Pakistan and India, which unfortunately did not contain a citation and appears to have been since withdrawn or removed. I was following up on it with some documentation. The Siddi are primarily of Bantu ancestry, according to "Indian Siddis: African Descendants with Indian Admixture" in the American Journal of Human Genetics.
This particular paper — which is by geneticists, one should note, not historians, but which references the latter — establishes the background of the Siddi population thusly:
The first documented record of Siddis in India dates to 1100 AD, when the Siddis settled in Western India.^2,3 By the thirteenth century, substantial numbers of Siddis were being imported by the Nawabs and the Sultans of India to serve as soldiers and slaves. The major influx of Siddis occurred during the 17th–19th centuries, when the Portuguese brought them as slaves to India.^2
It is worth noting that this historical background here comes from a 1970 paper by the anthropologist (?) D. K. Bhattacharya in volume 10, issue 40 of Cahiers d'Études Africaines, and might have been made redundant by more recent research.
If I can piggyback onto this question with another question:
Is it true that the Arabic slave trade is still really a barely studied topic?
I had a prof around 2-3 years ago who talked about how he wanted to do some more research because it was a relatively new field.
At the risk of asking an overly simplistic question, I must ask; what was it exactly, or with a high degree of probability, as to why Africa became the "go-to" piece of geography to go and take people and place them into slavery?
I cannot see how it would be that learned from tribal warfare, that it can be enriching to steal your rival tribal enemies via warfare; plunging and pillaging enemies and enslaving them is a practice as old as civilization.
Could it be that it seems that our iteration of humans "sprang forth" in Africa, and the global immigration as people roamed to new lands, just triggered a steady high volume of people surging out of Africa?