I apologize up front, because this is going to be a long, rambling and confusing question, but here goes:
With a high degree of certainty, I can trace one branch of my family tree back to one Daniel Rich (1816 - 1890). For clarity, I will call him Daniel Jr., even though I don't know if that is accurate. The issue arises with his parents and his potential connection to one John Rich/Johannes Reich, which I will get to.
First, a brief map showing the geography of the area in question, the northern Vermont/New Hampshire Border region:
Now, the first half of the story, working backwards from present:
According to his death certificate, Daniel Rich Jr. was 74 years, 2 months and 28 days old when he died on June 30, 1890, which would make his date of birth April 2, 1816, in Lyme, NH (which is south of the area shown in the map above). [As an aside, note the cause of death - anthrax. I assume he farmed sheep]
Now, you will see that his father is listed as Daniel Rich as well, I'll call him Daniel Sr., born in Northumberland, NH, and his mother is listed as Nancy Marshall, born in Stark, NH. So far, so good.
Now, things start to get a bit difficult. I can't find a birth certificate for Daniel Jr. This area was still basically the frontier in 1816, so I'm not shocked by this. However, I also can't find any marriage license or birth records for Daniel Rich Sr. and Nancy Marshall. And they don't show up in the Census together either. However, there is a great deal of paperwork (marriage licenses of children, death certificates, Census, etc.) for one Daniel Rich and Sophia P. Chase. And, if you look on Find-A-Grave, you will find a Daniel Rich (1790 - 1868) who it was claimed was married to Sophia Prescott Chase around 1817 and who died in Northumberland, NH. But the list of children does not include anyone named Daniel.
So, what to do? Well, it turns out I may be able to approach it from the other direction. And so begins Part 2.....
The second half of the story, working forwards from the past.
Now, before anyone says it, yes, I know that one of the cardinal rules of genealogical research is that you don't start from some person you want to be related to and work your way forward trying to prove yourself right. However, family story has it that this part of the family is descended from John Rich (1729 - 1813) of Maidstone, Vt., who was a German immigrant born Johannes Reich. And, there is a great deal of information on him and his children thanks to this book: http://www.maidstone-vt.org/history. So, I figured I didn't have much to lose.
Anyway, John Rich had 9 children - 3 girls and 6 boys. Of the boys, one died as a toddler and one, named Daniel (of course!), died at age 20 with no kids. Of the 4 remaining boys, only 1, Jacob Rich (1770 - 1827), had a son named Daniel. So he is the only possible direct connection between John Rich and Daniel Rich Jr. from above. But, once again, I can't find birth, marriage, or death records for him.
But wait, there's more! In an effort to fill in the gaps, I read the article on Maidstone, Vt. in the Vermont Historical Gazetteer, Volume 1 (https://archive.org/details/vermonthistorica01heme/page/n1061). You will note that this article is written by Moody Rich (1780 - 1873), who was Jacob Rich's brother and Daniel Rich's uncle. However, he only would have been about 10 years older than Daniel. Why is this age gap important? Because on page 1028, Moody recounts a tale of how the wife and daughter of Caleb Marshall escaped the Indians. And then he mentions that he later married that daughter, who I know from other sources to be Sally Marshall. And it turns out that Sally had a younger sister named Nancy Marshall (born 1792)! Now the book also mentions that that Nancy Marshall married George Washington Byron sometime after 1824, but it does not mention any relationship between Nancy and Daniel Sr.
Finally, the summary!
First, if you actually made it this far into the question, kudos, you are more patient than I am. Anyway, what do we have?
Known Ancestor - Daniel Rich Jr., son of Daniel Rich Sr. and Nancy Marshall
Suspected Ancestor - Daniel Rich, son of Jacob Rich, but married to Sophia Chase.
Connection - Moody Rich, younger brother of Daniel Rich, married to Sally Marshall, who had a younger sister named Nancy Marshall.
Which leads to several questions:
1. Is Nancy Marshall, the mother of Daniel Rich Jr., the same person as Nancy Marshall, sister of Sally Marshall?
2. Is Daniel Rich Sr. the same person as Daniel Rich, son of Jacob Rich?
3. If the answer to both of the above is "yes," what was the nature of the relationship between Daniel Rich Sr. and Nancy Marshall? There is no evidence that they were married, and both were married to other people shortly after Daniel Rich Jr. was born. A quick marriage followed by a divorce or annulment seems incredibly unlikely in 1816. An out of wedlock birth is certainly the most obvious possibility, but if that is the case, how likely is it that the resulting child would know not only his mother's real name, but also her place of birth (for the death certificate)? How common and accepted were out of wedlock children in early 19th century frontier New England?
I don't expect anyone to actually know the answers to these questions of course, but I was hoping I might get some good suggestions on how I might approach finding the answers to these questions.