In my study of Somali history, I found online academic sources to be almost non-existent for the 18th century, although there is a considerable amount of work focusing on the period found in print. In contrast however, there is a wealth of information in the oral histories which I do have access to as a Somali speaker on this period, such as the fall of the Ajuuran, the Geledi ascendancy, Omani encroachment, and some notable clan wars and infighting in the Majeerten clan-state and the Gal-Madow wars and Somali push to the Tana river. Little of this seems to have been published anywhere for the most part.

But if you would like any recommendations in print, I would put forth

"Somali Sultanate: A History of the Geledi City-State Over 150 Years" by Virginia Luling (2002), "The Shaping of Somali Society: Recontructing the History of a Pastoral People, 1600 - 1900" (1982) "The Benaadir past: Essays on Southern Somali History" (1983), and "Patterns of Trade and Politics in the Somali Benadir, 1840-1885" (1969) by Lee. V Casssnelli.

All 4 works have a focus on the Somali early modern period (1540-1850), but 3 of them exclusively focus on southern Somalia and the Benadir coast and not the rest of Greater Somalia, while "The Shaping of Somali Society: Reconstructing the History of a Pastoral People, 1600 to 1900" focuses on the whole of Greater Somalia and the dominant Somali ethnic group and not the southern Somaliazed Perso-Arab and Bantu minorities.

I personally would not recommend I.M Lewis for his historical works, but moreso for his solid analysis on Somali society and sociopolitic. His works are far too outdated and very orientalist, and are better fit to be seen as fictitious storytelling than any backed and evidenced history. So while a fine anthropologist, he is a truly awful historian.

Online? You won't find much. I. M. Lewis's A Modern History of the Somali ("revised, updated, expanded") is still the standing work, with the newest edition in 2003--but a lot of the material hasn't changed since first publication over 50 years ago. I'll see if there are any newer works on parts of the country--it depends on which area you want, because "Somalia" is cobbled together as an entity. Northeast African Studies (the journal) might be another place to look, but again, there's not going to be much if anything online.

I have found some stuff on Jstor, but it is pretty peripheral to the early modern era.

Neville Chittick wrote an article called medieval mogadishu for Paideuma in 1983, which is widely cited. It looks at the development of that city from an architectural, trade, and religious context. The title is a tip-off that this article focuses more on the 11th to 16th centuries, so a little bit before you are looking for.

Further back in the early 1960s, G.S.P. Freeman Granville wrote an article about the coins of the Mogadishu sultanate from 1300 to 1700. It does get into the era that you have expressed interest in. However, being focused on numismatics, it does have a fairly constrained focus.

Perhaps most relevant to your interest is Muqdisho in the Nineteenth century; A regional perspective by Edwin Alpers.

Otherwise, you could check out Archaeology of Islam in Sub-Saharan Africa by timothy insoll. He does devote some attention to the Adal sultanate and Berbera in the 15th and 16th centuries. Again, this is a bit earlier than you are looking for, I think.

My only other advice would be to use more specific terminology in your searches. Search for Berbera/Barbara, Hargeisa, Mogadishu, Benadir, or the Mogadishu sultanate, or the Sultanate of Aussa, the Ajuran sultanate, or the Warsangali sultanate.