The Pushkantser family tree  has 1000 people in it and goes back to about 1740. The family came from the village of Rumsiskes (Rumshishok) in the Lithuanian region of Russia . The earliest record of the Pushkantser name is 1842 in a taxpayers list  which lists 7 Pushkantsers.
The family tree  says that the first Pushkantser to come to the US was Abram Hirsh (Harris) in about 1878. He shortened his name to Kanzer and settled in Brooklyn, NY. His brother Henry later adopted the same surname. The second Pushkantser immigrant was another brother Chaim-David (b. 1836) in 1882, who stayed in New York. The third was Jacob Biniamin (Benjamin) Yankel, also in 1882. When he applied for citizenship in Albany, NY in 1887 he used the name Poskanzer. All subsequent family immigrants to Albany took the name Poskanzer. The fourth immigrant was Eliash-Hirsh in 1889 who adopted the name Rosenberg. About 1900 a branch of the family migrated to Novofastov, Vinnitsa (Vinnytsya) district, Ukraine region of Russia, not far from Kiev. They kept the name Pushkantser and recently dispersed all over the world including the USA.
Pushkantser, so far as we know, is a mono-genetic name. Mono-genetic names are those that appeared only in one particular place at one specific moment in one particular family. That is, everyone with this surname has the same progenitor .
"A Dictionary of Jewish Surnames from the Russian Empire"  by Alexander Beider says that the surname Pushkantser came from the place name Pushkantsy (Russian). Beider, who lives in Paris, told me that Russian Pushkantsy = Polish Puszkance = Lithuanian Puškanciai, and that Puszkance should be in the 1888 Polish gazetteer . I found the 15-volume gazetteer on microfilm at the Family History Library at the Mormon Temple in Oakland CA and indeed it was there. It says that Puszkance was a village in the district novoaleksandrovsk in the 5th Polish region 50 miles from Zarasai, but it did not say in which direction. In the gazetteer there are many similar names beginning with "Pa" [7, 8], but Beider says "I believe that if Russian/Polish spelling starts with "Pu", the Lithuanian one should also start with "Pu", not with "Pa". Then Beider wrote me on 8 Jan 06 that "Last week I was in Moscow and consulted the most detailed gazetteer of the Kovno (Kaunas) guberniya compiled in 1903. It lists two villages of Puszkance, both in the district of Novo-Aleksandrovsk, for both the closest railway station is Rakishki (Rokiskis in Lithuanian). The first one was situated in the subdistrict of Chadossy, 54 miles from Zarasai, had 29 inhabitants in 1903. The second one was situated in the subdistrict of Kvetki, 62 miles from Zarasai, had 30 inhabitants in 1903. One of them was the source for your surname." We now know that the villages were close to Rokiskis. The Earth Sciences Map Library on the UC Berkeley campus has the complete set of maps of western Russlands . Three miles south of the Rokiskis train station I found Pushantzy, which must be one of the villages. Beider agrees: "The map in question presents an erroneous spelling: the village called Pushantzy was undoubtedly actually called Pushkantsy". The other village I could not find. The one I found would be in modern coordinates at latitude N55° 53' 40" and longitude E25° 34' 10". Today there is not much there. A problem is that this location is only 30 miles from Zarasai. It is 90 miles NE of Rumsiskes. Of course we do not known if the first Pushkantser came from this location, or if the name of that village was just used when the Tsar required all jews to chose a surname in the early 1800s.
The Grand Duchy of Lithuania Research Project  has a record from 1784 of Puszkance/Puszkancz in the Birzai Kahal, Upyte/Pamevezys district, also at one time in the jurisdiction of Pandelys/Ponedel. Only one family is shown to be living there, but the names do not match what we know of the Pushkantser family at that time. We have not been able to locate the corresponding modern village. However, a village in that district might have been one of the same villages referred to above.
Thus one of these Puszkance/Pushantzy villages, found in three references, very probably was the source for the surname Pushkantser, as described by Beider.There are also more detailed earlier notes on the search for the village of Puszkance.
Art Poskanzer, with great help from Alexander Beider, Sonia Hoffman, and Olga Zabludoff