Assalaamu alaykum. I read a narration in Musnad Abu Ya’la Al-Musli, hadith no. 4788, in which ‘Aa’ishah, may Allaah be pleased with her, said that the Prophet, sallallaahu 'alayhi wa sallam, led them three nights in the Taraweeh prayer with 11 rak’ahs. Is this particular narration sound? May Allaah reward you.

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

The hadeeth that you mentioned was reported by Abu Ya’la; it reads as follows:

“Haroon ibn Ma’roof narrated to us from Ibn Wahb from ‘Abdullaah ibn 'Umar from Abu an-Nadhr from Abu Salamah from ‘Aa’ishah that the Prophet went out one night in Ramadan to the mosque after the ‘Isha prayer and prayed, and some men saw him and prayed behind him. The second night, he went out to the mosque, and the people saw him, so they returned to the mosque and prayed behind him. On the third night, the mosque was full with a large number of people, but the Prophet did not come out to them. So the people wanted to incite his coming out to them, and he said, 'O ‘Aa’ishah, what do the people want?' I [‘Aa’ishah] said, 'O Messenger of Allaah, they prayed with you those two nights so they want you to go out to them [to lead them in prayer];' then he went out to them and said, 'O people! You should perform only the acts that you can afford to perform, as Allaah is not bored until you get bored; and the most beloved actions to Allaah are the ones that are done continuously, even if they are little. I was afraid that the night prayer would become obligatory on you if you perform it continuously.' ‘Aa’ishah said, 'The Prophet used to pray eleven rak’ahs while standing up, and two rak’ahs while sitting down, and when he wanted to bow for rukoo’, he would stand up and recite for a little while and then he would perform rukoo’; and then he performed the Witr prayer one rak’ah.' Abu Salamah said, 'I asked her: How was his prayer in the month of Ramadan?' She said, 'He did not perform in Ramadan more than this number.''”

Shaykh Husayn Saleem Asad ruled that this hadeeth is dha'eef (weak). However, the story of the Prophet performing the prayer two nights with the people in Ramadan is confirmed in Saheeh Al-Bukhari and Saheeh Muslim:

‘Aa’ishah narrated that, once, in the middle of the night, the Prophet went out and prayed in the mosque, and some men prayed with him. He prayed on the second night, and more people gathered and prayed with him. On the third or fourth night, the number of people increased greatly, but the Prophet did not come out to them. The next morning, he came out to them and said, “I saw what you did; I did not come out to you only because I was afraid that the night prayer would become obligatory on you.” This was in Ramadan.

Allaah knows best.