The Prophet ﷺ used to recite in the dawn prayer on Friday "Alif Lam Mim. The revelation" [Sajdah 32:1–2] and "Has there come upon man" [Insan 76:1]. The Prophet ﷺ used to recite in the Friday prayer Surah al-Jumuah and Surah al-Munafiqun.
أن النبي ﷺ كان يقرأ في صلاة الفجر يوم الجمعة: {الم تنزيل} و {هل أتى على الإنسن}. وأن النبي ﷺ كان يقرأ في صلاة الجمعة سورة الجمعة والمنافقين.
Muslim narrated it in the Jumuah chapter (879) through several routes from Mukhawwal bin Rashid, from Muslim Batin, from Saeed bin Jubayr, from Ibn Abbas, and he related it.A similar narration has been reported from the hadith of Ibn Masud, but it is not sahih. Tabarani narrated it in Awsat (958, Majma Bahrayn edition). It contains Tabarani's teacher Muhammad bin Bishr bin Yusuf Umawi Dimashqi, whom I have not found either affirmed or criticized regarding his reliability. It also contains Walid bin Muslim, who is well known for the tadlis of leveling (tadlis al-taswiyah), and he did not state explicitly throughout the entire chain. Abu Ishaq Sabi is also a mudallis, and he narrated with the ambiguous form ("an"). And Allah knows best.As for what Bayhaqi narrated in Sunan al-Kubra (3/201) through the route of Saeed bin Simak bin Harb, who said, my father narrated to me, and I do not know it except from Jabir bin Samura, who said, "The Messenger of Allah ﷺ used to recite in the Maghrib prayer on the night of Jumuah, "Say, O disbelievers" and "Say, He is Allah, the One". And he used to recite in the last night prayer (Isha) on the night of Jumuah, Surah Jumuah and Munafiqun."This is extremely daif, for Saeed bin Simak is one whose hadith is abandoned, and his father Simak bin Harb was truthful but his memory deteriorated toward the end of his life, and he used to be prompted (with what to say). For more, see Minna Kubra (2/225).