This hadith was reported by an-Nasa’i (1268), and it is authentic.
However, in Ahmad bin Sa’id al-Ashbahi’s in ‘al-Bisharah fi Shudhudh Tahrik al-Isba’ fi at-Tashahhud wa Thubut al-Isharah’ (p. 72), it is mentioned that the wording of “…and I saw him moving it…” of the chain containing Za’idah bin Qudamah contradicts the wording of the chains of Bishr bin al-Mufaddal, Sufyan bin ‘Uyaynah, Sufyan ath-Thawri, ‘Abd al-Wahid bin Ziyad, Shu’bah, Zuhayr bin Mu’awiyah, ‘Abdullah bin Idris, Khalid bin ‘Abdullah at-Tahhan, Muhammad bin Fudayl, Abu al-Ahwas Sallam bin Sulaym, Abu ‘Awanah, and Ghilan bin Jami’ - all of these narrators reported it from ‘Asim bin Kulayb from his father from the Companion Wa’il bin Hujr, and none of them described the Prophet as having moved his finger during the tashahhud.
In other words, since this same hadith was reported through thirteen other chains of narration, and none of the routes of narration mention the phrase “…I saw him moving it…” except for one, this specific phrase is considered a shadh addition that is to be disregarded, while the rest of the hadith is authentic and is to be acted upon, as was also opined by Muqbil al-Wadi’i.
In support of this position, an-Nawawi said in ‘al-Majmu” (3/398):
“And should one move his finger when lifting it to point with it? There are several opinions on this. The correct one - which is the clear opinion of the majority of scholars - is that one should not move his finger, and if he does happen to move it, this is makruh and does not nullify his prayer due to it being a minor movement. The second opinion is that it is haram to move his finger, and his prayer is nullified if he moves it…and this is a weak opinion. The third opinion is that it is mustahabb to move it, and their proof for this is the hadith of Wa’il bin Hujr in which he described the Messenger of Allah placing his hands in the tashahhud, saying: “Then, he would raise his finger, and I saw him moving it to make supplications.” This was reported by al-Bayhaqi with an authentic chain, and al-Bayhaqi said: “It is possible that what is meant by ‘moving it’ is that he lifted it up to point with it, not that he would move it repeatedly.”"
Ibn Qudamah al-Maqdisi said in ‘al-Mughni’ (1/524):
“…One should point with his index finger upon mentioning Allah in the tashahhud due to what we have narrated, and he should not move it.”
‘Uthman bin Ahmad al-Hambali said in ‘Hidayat ar-Raghib li Sharh ‘Umdat at-Talib’ (p. 126):
“…So, he should raise his finger without moving it around in the tashahhud and while supplicating in his prayer…”
Ibn Hazm al-Andalusi said in ‘al-Muhalla’ (4/151):
“And we prefer that when the one in prayer sits for the tashahhud, he points with his finger and does not move it.”
This was also affirmed by Muqbil al-Wadi’i in ‘as-Sahih al-Musnad’ (2/265).
And Allah Knows best.