Trying to figure out if my widowed great grandmother Anna M. Glynn grew up as an orphan or had maybe a step father.

Gynn is a family name in Cornwall. It is a version of the same name. My eldest son has Gynn as his first name his great grandmother's surname because the Gynn surname is dying out. Rumour has it that the Gynn family from Tresmarrow in Cornwall are descendants of the Charles Stuarts. I think also that Glynn is a welsh variant that surname. So try looking for GYNN.

Thank you for the suggestion about looking up my great grandmother's last name by trying different spellings like with Gynn instead of Glynn. :-)

I can give you two suggestions but they are long shots.

Anna M Glynnn probably stands for Anna Maria Glynn. As the use of the combination Anna Maria was common at the time.

Then maybe the girl was called Maria or Mary. You could try these on the 1901 Census. I see one for Gort.

The civil Registrations can be searcher in Familysearch.org Go to Search, enter her name location Ireland and enter years 1890 to 1900. You might spot something here. 

I just noticed you mentioned Mayo. The registration districts fro Mayo are Ballina, Ballinrobe, Belmullet, Castlebar, Castlereagh, Claremorris, Killala, Newport, Swinford and Westport. You can use these in your location search in Familysearch.orrg. I already see one anna Glynn 1896 for Claremorris.By any chance did they emigrate before the 1901 Census?

So far on familysearch.org I found:

           https://familysearch.org/pal:/MM9.1.1/FBN8-ZT1
Name: Anna Maria Glynn
Event Type: Birth
Event Date: Jan - Mar 1897
Event Place: Kilmallock, Ireland
Registration Quarter and Year: Jan - Mar 1897
Registration District: Kilmallock
Age:
Birth Year (Estimated):
Mother's Maiden Name:
Volume Number: 5
Page Number: 281
GS Film number: 101066
Digital Folder Number: 004193980
Image Number: 00366
Collection: Anna Maria Glynn, "Ireland, Civil Registration Indexes, 1845-1958"

and on http://www.census.nationalarchives.ie/pages/1901/Limerick/Kilmallock/Ki…;

    while searching the 1901 census records in Ireland for my great grandmother Anna glynn it shows that in Limerick county her first name ended with the letter e instead of a, could be that her first name was mispelled when the census was taken. It makes me wonder if someone in my family tree had a learning disability perhaps with Dyslexia; even when it comes to writing and spelling. I have been learning disabled all my life and had a real hard time with math in school. The more pieces I find for my family tree puzzle the better.

                                                                 Francis John Nolan

This is a link to the site that will give you details of how you can order a cert. They may be able to email one to you for 4 euro. On the other hand you may have to pay postage and wait for same. If you email them the information from Family Search .org they should be able to source the original cert for you which will have much more information.

http://www.groireland.ie/research.htm

But first have you exhausted the information you can collect on your side. Emmigration records, Naturalisation records, You do not state what state she resided in. Is there a marriage record that might give name of her father. Does her death record reveal any vital information to her place of origin. The more you can tell us the easier it is on this side.

The only vital records I have so far on Anna is the document she signed for my great grandfather's headstone at the HolyCross cemetary in New Jersey and the baptism record from her first born son. The baptism record of her first born son shows her name as Anna glynn and her husband as John James Nolan. The only copy I can show you as an attachment from Anna's vital records is the one that shows her signature on the document for my great grandfather's headstone. The one for the baptism record I do not have because through ancestry.com my mother would have to order a copy seperately and neither me or my mother have the money yet to do so. Also my mother is not sure if thats the right one.  In the meantime I have been looking at public photos on ancestry.com from Glynn family trees that other people have put together to see if I can find anyone that has a close resemblance to my father, brother or sisters, which I know its not easy to do.  My great grandfather John James Nolan was a military veteran that was in ww1 or ww2, he died on the 5th of December in 1942.

                                                                                    Francis John Nolan