Hello again!
And here are the ruling authorities. I could only find some wikidata items for the main branch in Mawsil.
Lines 59 to 80:
https://docs.google.com/spreadsheets/d/17Cp1TyzOXknGDZu8_YCmwgd4gS56GvxvIATQW40rYmM/edit?usp=sharing
Aleppo, City of
Uqaylid occupation, 1079-1085 (https://www.acsearch.info/search.html?id=6689188)
Sharaf al-Dawla Muslim, 1079-1085 (https://www.acsearch.info/search.html?id=6689188)
Balad, Uqaylids of
Qutb al-Dawla Abu Mansur, circa 1004-1010 (https://www.zeno.ru/showphoto.php?photo=311275)
Najdat al-Dawla, circa 1015 (https://www.zeno.ru/showphoto.php?photo=177375)
Banu Uqayl dynasty
Muhammad bin Safwan, 888-889 (https://www.zeno.ru/showphoto.php?photo=303792)
Barqa'id, Uqaylids of
Ibrahim ibn al-Rajih, circa 1000-1009 (page 100 - C760 AR dirham, Barqa‘id mint only)
Abu'l-ujalla Rifa ibn Dhubay'a, 1013-1020 (https://www.zeno.ru/showgallery.php?cat=10047)
Mawsil, Uqaylids of
Muhammad ibn al-Musayyab, circa 990-996 (page 100 - 753 AR dirham )
Husam al-Dawla al-Muqallad ibn Musayyab, 996-1001 (https://www.acsearch.info/search.html?id=1490866)
Mu'tamid al-Dawla Qirwash ibn al-Muqallad, 1001-1050 (https://www.acsearch.info/search.html?id=1590428)
Ali ibn Muslim, 1089-1092; 1093-1096 (https://www.acsearch.info/search.html?id=9880334)
Nasibin, Uqaylids of
Janah al-Dawla 'Ali ibn al-Musayyab, 996-1000 (https://www.acsearch.info/search.html?id=3363382)
Sinan al-Dawla Abu Amir al-Hasan ibn al-Musayyab, circa 998-1003 (https://www.zeno.ru/showgallery.php?cat=10034)
Nur al-Dawla Abu Mus'ab, 1003-1006 (https://www.zeno.ru/showgallery.php?cat=10035)
Abu'l-Fadl Badran, 1015-1021 (https://www.acsearch.info/search.html?id=1490868)
Mu'tamid al-Dawla Qirwash ibn al-Muqallad, 1020-1021 (https://www.acsearch.info/search.html?id=1590429)
Sinjar, Uqaylids of
Abu'l-Mujallah Jirji ibn Qumayd, circa 1000-1012 (https://www.zeno.ru/showgallery.php?cat=13983)
Takrit, Uqaylids of
Abu'l Hawwad Hammad ibn Ahmad, governor, circa 990-999 (page 100 - N757 AR dirham, Tikrit only)
Muzahir al-Dawla Rafi' ibn al-Husayn, circa 1009-1033 (https://www.acsearch.info/search.html?id=3099763)
Ukbara, Uqaylids of
Kamal al-Dawla Gharib, 1011-1034 (https://www.zeno.ru/showphoto.php?photo=235340)
Uncertain Uqaylid region
Shihab al-Dawla Abu Darra, circa 1009 (page 101 - D760 AR dirham, al-Jazira 399 only, citing the Buwayhid ruler Baha’ al-Dawla, no other ‘Uqaylid)
'Izz al-Dawla, circa 1035-1054 (page 101 - 760D AR dirham, known only from Awana 426)
(https://www.acsearch.info/search.html?id=10151674)