[Hat tip Benson]
This is from here.
Starting from Rosh Chodesh Ellul till Shmini Atzeres , there is a Minhag to say twice a day
”Ledovid Hashem Ori”.
This Minhag is not mentioned in Shas, Shulchan Aruch, Kisvi Ha’ari Zal or in the original Machzorim.
One of the first Poskim who brings this Minhag, is the Mateh Efrayim. (R. Efrayim Zalmen Margulios).
There were Chasidic dynasties who didn’t follow this Minhag. (Choze Milublin , Zidichoiv, Apte, Sanz & Ropshitz.
The Ma’ase Rav writes that the Vilna Gaon didn’t say it. Today almost all Yeshivishe and
Chasidishe Minyonim, do say it. The one exception is, Chasidim from the Sanzer dynasty.
(Bobov, Klausebburg etc.)
There are different reasons given for not saying it. The true reason is, because
The first mention of this Minhag, is brought down in a Sefer called “ Chemdas Yomim”.
The Chemdas Yomim was probably the one who started this Minhag.
The Sefer Chemdas Yomim has no name of the Mechaber (Author) on the Shar Blatt.
The Yavetz and many Chassidic Rebbes, claimed that the Mechaber was Nosson Hoazosi
(Nathan from Gaza). Nosson Hoazosi was Shabsai Zvi’s Novi Sheker and right hand man.