3 ("my emails dated Jan. 15' reception") is certainly incorrect. A final apostrophe can only ever be used to mark the "Saxon genitive" when it comes directly after an /s/ or /z/ sound.* In other contexts, the "Saxon genitive" marker has to be written as <'s>, even when the head noun is plural: note that we write children's, not children'.
So if you must use either 2 or 3, 2 would be preferable (but not good, for reasons mentioned in the comments: it sounds very unnatural to me).
*There are also other, more complicated criteria that further restrict the use of the final apostrophe: for example, even though the irregular plural noun geese ends in /s/, the plural possessive has to be written as geese's (pronounced /giːsɨz/). In some contexts, the usage of <'> vs. <'s> is not uniform, even for educated speakers.