Hi Klonie
We have DNA tests that prove that Stockbridge is NOT Amasa's father, but they don't prove that Olivia (or one of the daughters is not the mother).
The Beem family history is all based on what Amasa did or did not tell his family in Indiana, so that's really a dead end.
If I remember correctly, there is some sort of record that family (a cousin) from Hanover Mass visited the Joslins in Indiana some time after Amasa's death (that is, after 1844), which at least establishes a link with the family back in Massachusetts.
Amasa could have been a foundling, although its hard to imagine the Josselyn family taking in a new unrelated baby at that point in their lives. That seems to point to one of the daughters becoming pregnant and Amasa being raised by Olivia (Stockbridge's wife) as a son. There is some indication that Stockbridge is not living with the family at that point.
Then when Olive (the eldest daughter) married and moved away, and Olivia dies (1803) that Amasa moved to live with Olive in New York.
The problem is pinning it all down.