The NTA Film Network wasn't really a network as we usually think of it...it was a syndicator of filmed shows and old movies, including a lot of the old pre-1948 Fox film library (NBC got the post-1948 Fox library in a 1961 deal that created the Saturday Night at the Movies series). National Telefilm Associates was a prominent player in recycling films and off-network reruns in the 50s and 60s, and also owned WNTA (New York market Channel 13) in the same time frame, programming their station with the same stuff they were selling to stations like CKLW-TV in other markets. In the late 1950s they even tried their hand at producing and distributing some original series in syndication, in partnership with the 20th Century Fox studios. They marketed them under the "NTA Network" banner although they were never simultaneously fed to or aired by stations over what we'd think of as a network line. None of the first run shows lasted more than a couple of seasons and none of them are being rerun today.
NTA's business plan worked OK for a while but petered out in the early 60s, and the company had to sell its New York station to a nonprofit company wanting to bring noncommercial educational TV to the city. That station's now WNET, one of the key producing stations in the PBS system.
A series of transactions, sales and mergers over the last 30 years has left NTA disappearing into the Republic Pictures organization with rights to some of its film properties now held by Viacom's Paramount Pictures, some reverting to the Fox network, and some in the hands of CBS.