How can I identify who my maternal grandfather was through autosomal DNA testing?
My mother was born in 1928 and is deceased.
She had no full siblings. I have taken a DNA test on Ancestry.com, and have also registered on GEDmatch.
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It will help if your father is still alive and willing to test. If not, consider his siblings or your first cousins on that side.
Your best hope is to find DNA first or second cousins, but work with what you've got. This requires a lot of luck, though you already know there will be no maternal first cousins (if she had half siblings, then test them!). Then see if they match your dad or your dad's close relatives. If they don't, then the match is on your mom's side (note: if you have your dad's DNA you can say for sure if the match is from your mom's side, but with cousins or uncles/aunts, it may not show up if it's 3rd cousin plus).
Your chances of this working improve if your siblings and all known relatives on your mom's side test. This includes your mom's mom's side, so you can rule out that line with matches. (Note: there is no need to test your children or the children of any siblings/cousins you have DNA for.)
Once you find some cousins on the correct line, you'll still have to do traditional paper trail genealogy to find your grandfather candidates.
It's a long slog. Some people get lucky straight away, but that's not real common. Use a good family tree program (not Ancestry, because you want to include living people and add a lot of notes, some of which will need to be private) and write down your findings from DNA matching.