Salamu Aleikum
Is this hadith saheeh? And is it complete or is there something missing?
The Holy Prophet (SAWS) said: When Adam committed his mistake he said: O my Lord, I am asking you to forgive me for the sake of Muhammad. Allah said: O Adam, and how do you know about Muhammad whom I have not yet created? Adam replied, O my Lord, after You created me with your hand and breathed into me of Your Spirit, I raised my head and saw written on the heights of the Throne: "LA ILAHA ILLALLAH MUHAMMADUN RASULULLAH" I understood that You would not place next to Your Name but the Most Beloved One of Your creation. Allah said: O Adam, I have forgiven you, and were it not for Muhammad I would not have created you."

All perfect praise be to Allah, The Lord of the Worlds. I testify that there is none worthy of worship except Allah, and that Muhammad is His slave and Messenger.

In some inauthentic narrations that were reported by At-Tabaraan, Al-Haakim and others, it was reported with different wordings that “When Aadam committed the mistake (of eating from the tree), he said: "O my Lord, I am asking you to forgive me for the virtue of Muhammad.” Allah said: “O Aadam, and how do you know about Muhammad whom I have not yet created?” Aadam replied: “O my Lord, after You created me with your Hand and breathed into me of Your Spirit, I raised my head and saw written on the heights of the Throne: “La Ilaaha Illallaah Muhammadun Rasoolullaah”; so I understood that You would not place next to Your Name but the most beloved one of Your Creation to You.” Allah said: “O Adam, you are right; he is indeed the most beloved one of My Creation to Me, ask me by his virtue, I have forgiven you; were it not for Muhammad, I would not have created you."

The scholars of Hadeeth, such as Ath-Thahabi, Al-Albaani and others, stated that this Hadeeth is fabricated.

Additionally, what was mentioned in the Hadeeth “…were it not for Muhammad, I would not have created you."; contradicts what is stated in the Quran that He created mankind and the jinn to worship Him, as Allah Says (what means): {And I did not create the jinn and mankind except to worship Me..} [Quran 51:56]

Allah knows best.