I don't know much about what the anti-Nicene church fathers held regarding the rapture(s) . . . and I would defer to @AdHoc regarding any teachings from back then about multiple/partial reapings. And even if no church father source for the idea comes from that period, I would maintain that this, in and of itself, certainly does not negate the idea.
I do agree that much of the partial rapture teaching did get promulgated by 19th century authors. Here's something from Wikipedia in an article on "Rapture" subsection "Partial pre-tribulation premillennialism": As stated by Ira David (a proponent of this view): “The saints will be raptured in groups during the tribulation as they are prepared to go.”[98] Some notable proponents of this theory are G. H. Lang, Robert Chapman, G. H. Pember, Robert Govett, D. M. Panton, Watchman Nee, Ira E. David, J. A. Seiss, Hudson Taylor, Anthony Norris Groves, John Wilkinson, G. Campbell Morgan, Otto Stockmayer and Rev. J. W. (Chip) White Jr. Found here - an interesting read on the whole matter of the rapture: https://en.wikipedia.org/wiki/Rapture
I am familiar with a number of these authors and many were in the 19th century.
If anyone is interested, here is a website I found today that promotes Partial Rapture Theory (PRT): https://www.bible-prophecy.co/partial-rapture-theory/ I have just started to look through it, so I can't vouch for its veracity. UPDATE: Just realized this website is by an author whose book I have on my shelf: "The Partial Rapture and the Left Behind Church" by Paul Shoenbarger