(Only this dialect will be dealt with extensively here.) This is the dialect of the Aramaic parts of the Jerusalem Talmud, of the aggadic Midrashim, the Palestinian deeds, the Aramaic documents of the geonic period (found in the Cairo *Genizah), and synagogue inscriptions discovered in Ereẓ Israel. The Palestinian Targum and the Targum Pseudo-Jonathan of the Pentateuch are written in a dialect which, for all practical purposes (except for a few details), is that of Galilean Aramaic.
Galilean Aramaic covers a period from the first amoraim of the Jerusalem Talmud (third century C.E.) to the last geonim(beginning of the second millennium C.E.). It seems (on the evidence of manuscripts), that the Aramaic of the Mishnah also very closely resembles (or is identical to) Galilean Aramaic.