.... Komnenos, of Trebizond

According to Thierry Ganchou, Manuel had one son by his second wife Anna. Ganchou identifies him as the otherwise nameless Komnenos whom George Sphrantzes mentions in his history.
This Komnenos had been the previous owner of the stallion Sphrantzes rode while campaigning in the Morea in 1429, and who married Eudokia the daughter of Manuel Palaiologos Kantakouzenos, but died before the couple could have children.[16]

• https://en.wikipedia.org/wiki/Manuel_III_of_Trebizond#Family

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-http://fmg.ac/Projects/MedLands/TREBIZOND.htm#KomnenosMEvdokiaKanta...

c) [--- Komnenos . His parentage is indicated by Georgios Phrantzes who records an incident during the siege of Patras, dated to 29 Mar 1429, when he rescued Konstantinos Palaiologos [the future Emperor Konstantinos XI] but was captured after falling from his horse, a thoroughbred which "ameras" [the emir, unspecified] had given to “Isaacio Asani” who had later given it to “Georgio Philanthropeno genero [%CE%B3%CE%B1%CE%BC%CE%B2%CF%81%CF%89] suo” who, in turn had given it to “Comneno consobrino [%CE%B1%CE%BD%CE%B5%CF%88%CE%B9%CF%89], Cantacuzeni protostratoris genero [%CE%B3%CE%B1%CE%BC%CE%B2%CF%81%CF%89]”[130]. One explanation for this person “Comneno” being “ανεψιω” of Georgios Philanthropenos is that the relationship was through Anna Philanthropena, second wife of Emperor Manuel III. The question has been explored fully in a recent article by Thierry Ganchou[131]. The circumstances of the flight of this person to Galata are unknown, but given the rivalries within the Trebizond imperial family it would not be surprising if he had considered that removing himself from the court was the option which better guaranteed his safety.

m (before 29 Mar 1429) EUDOKIA Kantakouzena, daughter of MANUEL Kantakouzenos & his wife ---. The Masarelli Vatican manuscript names Andreas and Eudokia as the children of Manuel & his wife, stating that Eudokia married a grandson of the emperor of Trebizond but died without issue[132]. Her marriage appears to be confirmed by Georgios Phrantzes who records an incident during the siege of Patras, dated to 29 Mar 1429, when he rescued Konstantinos Palaiologos [the future Emperor Konstantinos XI] but was captured after falling from his horse, a thoroughbred which "ameras" [the emir, unspecified] had given to “Isaacio Asani” who had later given it to “Georgio Philanthropeno genero [%CE%B3%CE%B1%CE%BC%CE%B2%CF%81%CF%89] suo” who, in turn had given it to “Comneno consobrino [%CE%B1%CE%BD%CE%B5%CF%88%CE%B9%CF%89], Cantacuzeni protostratoris genero [%CE%B3%CE%B1%CE%BC%CE%B2%CF%81%CF%89]”[133].]