There seems to be lots of them.
http://www.imperial-library.info/content/vehks-teaching
What is the relationship between the Psijic Order and the Psijic Endeavor?
Nothing but a namesake, I am sorry to say. Now we can end that mystery. The Endeavor is a method of achieving the Tower and then what to do after. The Order is not, and does not really care for the idea of the Endeavor at all, thinking it wrong-headed nearly from the start.
So what is the Psijic Order?
A monastic order of the Altmer, impressive with age, and obsessed with a kind of mythic genealogy, made famous by their monomythism. Theirs was mostly the study of reverse-ancestry as a means to combat spiritual and material degradation. Or at least it was, I should say, as I do not know what they do now and do not much care. They were wrong-headed nearly from the start.
It is interesting to note that their original views were very unorthodox for Altmer, and thus their exile from Alinor. These views included the suggestion that Anu’s son, the Time Dragon, was formed in reaction to Padhome’s influence. In effect, Anu had finally done something. This inconceivable effect gave rise to an equally inconceivable cause, and so PSJJJJ was named and the Order eventually took his name.
Veloth was not a member of these exiles, no. Some of the Order’s precepts and ideas do (or did) flourish in the beginnings of the Alessian Order, the Temple of the One in Cyrodiil, most Maruhkati sects (including the Selectives, though they would deny it), Ancestral-Mothism, and, most famous of all, the Mages Guild.
Note the Mages guild.
However are these counted as Psijjj? They are fundamentally different from how Psijjj usually is understood, still they have/had same name.