Many Sunni books narrated authentic Hadeeths from the Prophet Muhammad (SAWA) that Ali is the deputy and the successor of the Prophet (SAWA) e.g.
1. Musnad Ahmad bin Hanbal in Musnad Al-Asharah, Hadeeth 841: The Prophet said: Ali is my Khaleefa.
2. Musnad Ahmad ibn Hanbal, fadha'il al-Sahaba, Hadeeth number 1016: Ali is my Wasi .
3. Musnad Ahmed ibn Hanbal: It written on the gate of Paradise: LA ILAAHA ILLALLAH, MUHAMMAD RASOOLULLLAH, ALI AKHO RASOOLILLAH.
4. Al-Bukhari in his book Al-Tareekh Al-Kabeer vol. 1, p.375 that the Prophet (SAWA) said on the day of Ghadeer: For whom I am the master, Ali is his master.
5. Al-Albani in his book Takhreej Al-Hadeeth Al-Nabawi , Hadeeth number 94 that the Prophet said: Ali is the master of every of everyone who believes in me as his master.