Amram Ben Sheshna was gaon of Sura in the middle of the 9th century CE, when world Jewry (except, maybe, Israel) was most willing to accept the authority of the Babylonian academies. As a result, his responsa were highly influential.
The precise period during which he served in the gaonate is uncertain; however it is clear from one of his responsa that by 858 CE he was already acting in that capacity. More than 200 of Amram's responsa are extant. Some were in collections (and might, therefore have been corrupted). Others have been discovered in the Cairo Genizah. His responsa include both practical halachic decisions and comments on the Talmud. In one of them he states that it is prohibited to lend money to a non-Jew on interest, and even though indirect interest ("avak ribbit") is permitted, scholars should shun it.
Amram's fame, however, rests primarily on his Seder (commonly called his siddur), "the order of prayers and blessings for the entire year... according to the tradition which we possess, as laid down by the Tannaim and Amoraim."
The Seder, "Yesod ha-Amrami," originated in a responsum which was seemingly sent to the community of Barcelona. From there it spread throughout Spain and to other countries. The Seder Rav Amram is the oldest order of Jewish prayers extant. It contains the text of the prayers for the entire year, as well as the laws and customs pertaining to the different prayers.
Although Amram's predecessor Natronai had written a responsum (mentioned at the beginning of Amram's Seder) to the community of Lucena explaining how the rabbinic injunction to recite 100 blessings daily should be fulfilled and had established the sequence of weekday prayers, Amram was the first to compose a systematic arrangement including prayers for the whole annual cycle as well as the pertinent laws.
Amram's sources, in addition to the Talmud, were the works of the geonim and the rites of the Babylonian academies. The Seder enjoyed a very wide circulation and was extensively quoted by the leading scholars of Spain; Provence, France; and Germany. It served as the basis for later orders of service, such as Siddur Rashi, Machzor Vitry, and especially the liturgy of countries which came under Babylonian influence.
Rabbenu Tam (12th century) declared: "Whoever is not well-versed in Rav Amram's Seder and in Halachot Gedolot... dare not alter the words of the early authorities or their customs, for we must rely upon them wherever they do not contradict our Talmud but [merely] add to it. Many customs we observe originated with them."
Three different manuscripts of the Siddur are extant, and additional fragments have been discovered in the Cairo Genizah. The present work is not that written by Amram, and contains later interpolations. Moreover, a thorough study of the Seder, as well as a comparison between it and passages cited from it by the earlier rabbinic authorities, show that in the course of time changes were introduced into Amram's original text, both in the sections comprising the prayers and in those dealing with the laws.
Some scholars even maintain that Amram sent to Spain only the "order" of the prayers and blessings together with the relevant laws but not the actual text of the prayers and blessings, which were added later.
Sources: Gates of Jewish Heritage